Edit Profile (opens in new tab) Shanmugalingam, Nageswari Compute Distance To: Compute Author ID: shanmugalingam.nageswari Published as: Shanmugalingam, Nageswari; Shanmugalingam, N. Documents Indexed: 95 Publications since 2000, including 1 Book 1 Contribution as Editor Reviewing Activity: 3 Reviews Biographic References: 1 Publication Co-Authors: 62 Co-Authors with 86 Joint Publications 1,153 Co-Co-Authors all top 5 Co-Authors 10 single-authored 16 Björn, Jana 14 Björn, Anders 13 Korte, Riikka 10 Koskela, Pekka 9 Lahti, Panu 8 Kinnunen, Juha 7 Durand-Cartagena, Estibalitz 5 Tuominen, Heli 5 Tyson, Jeremy T. 4 Aikawa, Hiroaki 4 Jaramillo, Jesús Angel 4 Malý, Lukáš 4 Marola, Niko 3 Adamowicz, Tomasz 3 Alonso-Ruiz, Patricia 3 Baudoin, Fabrice 3 Eriksson-Bique, Sylvester 3 Lindquist, Jeff 3 Miranda, Michele jun. 3 Rogers, Luke G. 3 Teplyaev, Alexander 3 Zhou, Yuan 2 Gill, James T. 2 Hakkarainen, Heikki 2 Heinonen, Juha 2 Holopainen, Ilkka 2 Kilpeläinen, Tero 2 Li, Xining 2 Speight, Gareth 2 Xie, Xiangdong 2 Yang, Dachun 2 Yuan, Wen 2 Zhong, Xiao 1 Albin, Nathan 1 Bonk, Mario 1 Capogna, Luca 1 Estep, Dewey 1 Giovannardi, Gianmarco 1 Gogatishvili, Amiran 1 Hajł, Asz Piotr 1 Herron, David A. 1 Hoppis, Jared 1 Järvenpää, Esa 1 Järvenpää, Maarit 1 Jiang, Renjin 1 Jones, Rebekah 1 Juutinen, Petri 1 Kallunki, Sari 1 Kline, Joshua 1 Lehrbäck, Juha 1 Liu, Qing 1 Lorent, Andrew 1 MacManus, Paul 1 Minda, David 1 Poggi-Corradini, Pietro 1 Ponnusamy, Saminathan 1 Rajala, Kai 1 Rogovin, Kevin 1 Rogovin, Sari 1 Snipes, Marie A. 1 Williams, Alex 1 Zhou, Xiaodan all top 5 Serials 6 Journal of Differential Equations 5 Journal of Functional Analysis 5 The Journal of Geometric Analysis 5 Potential Analysis 4 Indiana University Mathematics Journal 4 Mathematische Zeitschrift 4 Revista Matemática Iberoamericana 4 Calculus of Variations and Partial Differential Equations 4 Annales Academiae Scientiarum Fennicae. Mathematica 3 Journal of Mathematical Analysis and Applications 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 The Journal of Analysis 2 Journal d’Analyse Mathématique 2 Arkiv för Matematik 2 Collectanea Mathematica 2 Illinois Journal of Mathematics 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Nachrichten 2 Michigan Mathematical Journal 2 Transactions of the American Mathematical Society 2 Advances in Calculus of Variations 2 Analysis and Geometry in Metric Spaces 1 Archive for Rational Mechanics and Analysis 1 Houston Journal of Mathematics 1 Advances in Mathematics 1 Canadian Journal of Mathematics 1 Commentarii Mathematici Helvetici 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Publicacions Matemàtiques 1 Notices of the American Mathematical Society 1 Mathematical Research Letters 1 Positivity 1 Revista Matemática Complutense 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 New Mathematical Monographs 1 Complex Analysis and its Synergies 1 Annales Fennici Mathematici all top 5 Fields 54 Potential theory (31-XX) 53 Functions of a complex variable (30-XX) 33 Functional analysis (46-XX) 16 Real functions (26-XX) 13 Measure and integration (28-XX) 12 Partial differential equations (35-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Differential geometry (53-XX) 6 General topology (54-XX) 3 Abstract harmonic analysis (43-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 86 Publications have been cited 1,720 times in 711 Documents Cited by ▼ Year ▼ Newtonian spaces: An extension of Sobolev spaces to metric measure spaces. Zbl 0974.46038Shanmugalingam, Nageswari 307 2000 Sobolev spaces on metric measure spaces. An approach based on upper gradients. Zbl 1332.46001Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 203 2015 Harmonic functions on metric spaces. Zbl 0989.31003Shanmugalingam, Nageswari 109 2001 Regularity of quasi-minimizers on metric spaces. Zbl 1006.49027Kinnunen, Juha; Shanmugalingam, Nageswari 105 2001 Sobolev classes of Banach space-valued functions and quasiconformal mappings. Zbl 1013.46023Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 77 2001 Quasicontinuity of Newton–Sobolev functions and density of Lipschitz functions on metric spaces. Zbl 1170.46032Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 55 2008 The Dirichlet problem for \(p\)-harmonic functions on metric spaces. Zbl 1018.31004Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 47 2003 Boundary Harnack principle for \(p\)-harmonic functions in smooth Euclidean domains. Zbl 1121.35060Aikawa, Hiroaki; Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao 41 2007 Lebesgue points and capacities via boxing inequality in metric spaces. Zbl 1146.46018Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 40 2008 Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces. Zbl 1003.31004Björn, Jana; MacManus, Paul; Shanmugalingam, Nageswari 37 2001 The Perron method for \(p\)-harmonic functions in metric spaces. Zbl 1039.35033Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 35 2003 Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari 35 2010 Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces. Zbl 1027.31006Koskela, Pekka; Rajala, Kai; Shanmugalingam, Nageswari 29 2003 Modulus and continuous capacity. Zbl 1002.31004Kallunki, Sari; Shanmugalingam, Nageswari 28 2001 Some convergence results for \(p\)-harmonic functions on metric measure spaces. Zbl 1034.31006Shanmugalingam, Nageswari 25 2003 Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces. Zbl 1132.46021Björn, Jana; Shanmugalingam, Nageswari 24 2007 Non-conformal Loewner type estimates for modulus of curve families. Zbl 1210.30020Adamowicz, Tomasz; Shanmugalingam, Nageswari 23 2010 Pointwise properties of functions of bounded variation in metric spaces. Zbl 1295.26012Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 21 2014 A characterization of Newtonian functions with zero boundary values. Zbl 1238.31008Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 21 2012 Stability and continuity of functions of least gradient. Zbl 1318.26028Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N. 18 2015 Singular functions on metric measure spaces. Zbl 1039.31016Holopainen, Ilkka; Shanmugalingam, Nageswari 16 2002 Measurability of equivalence classes and MEC\(_p\)-property. Zbl 1146.28001Järvenpää, Esa; Järvenpää, Maarit; Rogovin, Kevin; Rogovin, Sari; Shanmugalingam, Nageswari 16 2007 Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen. Zbl 1088.31005Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 16 2004 Regularity of sets with quasiminimal boundary surfaces in metric spaces. Zbl 1311.49116Kinnunen, Juha; Korte, Riikka; Lorent, Andrew; Shanmugalingam, Nageswari 16 2013 Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces. Zbl 1076.31006Aikawa, Hiroaki; Shanmugalingam, Nageswari 15 2005 The Dirichlet problem for \(p\)-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. Zbl 1341.31009Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 14 2015 Polar sets on metric spaces. Zbl 1078.31008Kinnunen, Juha; Shanmugalingam, Nageswari 14 2006 Prime ends for domains in metric spaces. Zbl 1297.30056Adamowicz, Tomasz; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 14 2013 Fine properties and a notion of quasicontinuity for BV functions on metric spaces. Zbl 1359.30055Lahti, Panu; Shanmugalingam, Nageswari 13 2017 Trace theorems for functions of bounded variation in metric spaces. Zbl 1392.26016Lahti, P.; Shanmugalingam, N. 13 2018 Characterizations of sets of finite perimeter using heat kernels in metric spaces. Zbl 1353.30054Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari 13 2016 Geometric analysis on Cantor sets and trees. Zbl 1376.46025Björn, Anders; Björn, Jana; Gill, James T.; Shanmugalingam, Nageswari 12 2017 Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Zbl 1278.30026Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari 12 2012 Sobolev extensions of Hölder continuous and characteristic functions on metric spaces. Zbl 1137.46018Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 11 2007 Comparisons of relative BV-capacities and Sobolev capacity in metric spaces. Zbl 1248.28002Hakkarainen, Heikki; Shanmugalingam, Nageswari 11 2011 Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces. Zbl 1307.30098Estep, Dewey; Shanmugalingam, Nageswari 10 2015 A rigidity property of some negatively curved solvable Lie groups. Zbl 1255.22005Shanmugalingam, Nageswari; Xie, Xiangdong 10 2012 Removable sets for the Poincaré inequality on metric spaces. Zbl 0958.30008Koskela, P.; Shanmugalingam, N.; Tuominen, H. 9 2000 The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces. Zbl 1211.49055Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 9 2010 Intrinsic geometry and analysis of diffusion processes and \(L^{\infty}\)-variational problems. Zbl 1302.60113Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 9 2014 Uniformity from Gromov hyperbolicity. Zbl 1189.30055Herron, David; Shanmugalingam, Nageswari; Xie, Xiangdong 9 2008 The \(\infty \)-Poincaré inequality on metric measure spaces. Zbl 1275.46018Durand-Cartagena, Estibalitz; Jaramillo, Jesús; Shanmugalingam, Nageswari 9 2012 Semmes family of curves and a characterization of functions of bounded variation in terms of curves. Zbl 1327.31026Korte, Riikka; Lahti, Panu; Shanmugalingam, Nageswari 9 2015 Preservation of bounded geometry under sphericalization and flattening. Zbl 1328.30019Li, Xining; Shanmugalingam, Nageswari 9 2015 Geometry and analysis of Dirichlet forms. II. Zbl 1297.53033Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 8 2014 Trace and extension theorems for functions of bounded variation. Zbl 1406.46025Malý, Lukáš; Shanmugalingam, Nageswari; Snipes, Marie 8 2018 Equivalence and self-improvement of \(p\)-fatness and Hardy’s inequality, and association with uniform perfectness. Zbl 1189.31006Korte, Riikka; Shanmugalingam, Nageswari 8 2010 Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces. Zbl 1333.30071Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari 8 2015 Notions of Dirichlet problem for functions of least gradient in metric measure spaces. Zbl 1434.31008Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari 8 2019 Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces. Zbl 1101.31008Juutinen, Petri; Shanmugalingam, Nageswari 7 2006 The Mazurkiewicz distance and sets that are finitely connected at the boundary. Zbl 1342.30054Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 7 2016 Hajłasz gradients are upper gradients. Zbl 1326.46035Jiang, Renjin; Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen 6 2015 \(p\)-Poincaré inequality versus \(\infty \)-Poincaré inequality: some counterexamples. Zbl 1255.46015Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari; Williams, Alex 6 2012 Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities. Zbl 07179616Ruiz, Patricia Alonso; Baudoin, Fabrice; Chen, Li; Rogers, Luke G.; Shanmugalingam, Nageswari; Teplyaev, Alexander 6 2020 Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces. Zbl 1318.42030Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen 5 2015 Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates. Zbl 1441.31007Alonso-Ruiz, Patricia; Baudoin, Fabrice; Chen, Li; Rogers, Luke; Shanmugalingam, Nageswari; Teplyaev, Alexander 5 2020 Geometric properties of planar \(BV\)-extension domains. Zbl 1196.46025Koskela, Pekka; Miranda, Michele; Shanmugalingam, Nageswari 5 2010 The Liouville theorem for \(p\)-harmonic functions and quasiminimizers with finite energy. Zbl 1456.35055Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 5 2021 Geometric characterizations of \(p\)-Poincaré inequalities in the metric setting. Zbl 1334.31007Durand-Cartagena, Estibalitz; Jaramillo, Jesus A.; Shanmugalingam, Nageswari 4 2016 On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 4 2001 A problem of Baernstein on the equality of the \(p\)-harmonic measure of a set and its closure. Zbl 1084.31008Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 4 2006 First order Poincaré inequalities in metric measure spaces. Zbl 1278.31012Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari 4 2013 \(L^\infty\)-variational problem associated to Dirichlet forms. Zbl 1280.49028Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 4 2012 Bounded geometry and \(p\)-harmonic functions under uniformization and hyperbolization. Zbl 1466.53048Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 4 2021 A universality property of Sobolev spaces in metric measure spaces. Zbl 1168.46306Shanmugalingam, Nageswari 3 2009 The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property. Zbl 1429.31009Adamowicz, Tomasz; Shanmugalingam, Nageswari 3 2019 Locally \(p\)-admissible measures on \(\mathbf{R}\). Zbl 1431.26012Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 3 2020 A characterization of BMO self-maps of a metric measure space. Zbl 1326.30050Kinnunen, Juha; Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari 3 2015 Quasiadditivity of variational capacity. Zbl 1293.31008Lehrbäck, Juha; Shanmugalingam, Nageswari 2 2014 Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity. Zbl 1392.31014Malý, Lukáš; Shanmugalingam, Nageswari 2 2018 Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient. Zbl 1427.31008Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari; Speight, Gareth 2 2019 Existence and uniqueness of \(\infty \)-harmonic functions under assumption of \(\infty \)-Poincaré inequality. Zbl 1420.31003Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari 2 2019 Traces and extensions of certain weighted Sobolev spaces on \(\mathbb{R}^n\) and Besov functions on Ahlfors regular compact subsets of \(\mathbb{R}^n\). Zbl 1480.46042Lindquist, Jeff; Shanmugalingam, Nageswari 2 2021 Maximal regularity via reverse Hölder inequalities for elliptic systems of \(n\)-Laplace type involving measures. Zbl 1158.35355Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao 1 2008 Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings. Zbl 1050.31008Shanmugalingam, Nageswari 1 2004 Hölder estimates of \(p\)-harmonic extension operators. Zbl 1131.35027Aikawa, Hiroaki; Shanmugalingam, Nageswari 1 2006 Modulus of families of sets of finte perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry. Zbl 1439.30089Jones, Rebekah; Lahti, Panu; Shanmugalingam, Nageswari 1 2020 Dichotomy of global capacity density in metric measure spaces. Zbl 1400.49004Aikawa, Hiroaki; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 1 2018 An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability. Zbl 1391.30068Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari 1 2018 Infinity modulus and the essential metric. Zbl 1401.30065Albin, Nathan; Hoppis, Jared; Poggi-Corradini, Pietro; Shanmugalingam, Nageswari 1 2018 An elementary proof of Cheeger’s theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces. Zbl 1345.31021Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari 1 2013 Special issue: Proceedings of the ICM2010 satellite conference and international workshop on harmonic mappings and quasiconformal mappings, HQM 2010, Madras, India, August 9–17, 2010. Zbl 1229.30003 1 2010 Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality. Zbl 1480.26004Durand-Cartagena, Estibalitz; Eriksson-Bique, Sylvester; Korte, Riikka; Shanmugalingam, Nageswari 1 2021 Rough isometry between Gromov hyperbolic spaces and uniformization. Zbl 1477.53074Lindquist, Jeff; Shanmugalingam, Nageswari 1 2021 Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry. Zbl 1477.30056Eriksson-Bique, Sylvester; Giovannardi, Gianmarco; Korte, Riikka; Shanmugalingam, Nageswari; Speight, Gareth 1 2022 Extension and trace results for doubling metric measure spaces and their hyperbolic fillings. Zbl 07485591Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 1 2022 Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry. Zbl 1477.30056Eriksson-Bique, Sylvester; Giovannardi, Gianmarco; Korte, Riikka; Shanmugalingam, Nageswari; Speight, Gareth 1 2022 Extension and trace results for doubling metric measure spaces and their hyperbolic fillings. Zbl 07485591Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 1 2022 The Liouville theorem for \(p\)-harmonic functions and quasiminimizers with finite energy. Zbl 1456.35055Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 5 2021 Bounded geometry and \(p\)-harmonic functions under uniformization and hyperbolization. Zbl 1466.53048Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 4 2021 Traces and extensions of certain weighted Sobolev spaces on \(\mathbb{R}^n\) and Besov functions on Ahlfors regular compact subsets of \(\mathbb{R}^n\). Zbl 1480.46042Lindquist, Jeff; Shanmugalingam, Nageswari 2 2021 Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality. Zbl 1480.26004Durand-Cartagena, Estibalitz; Eriksson-Bique, Sylvester; Korte, Riikka; Shanmugalingam, Nageswari 1 2021 Rough isometry between Gromov hyperbolic spaces and uniformization. Zbl 1477.53074Lindquist, Jeff; Shanmugalingam, Nageswari 1 2021 Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities. Zbl 07179616Ruiz, Patricia Alonso; Baudoin, Fabrice; Chen, Li; Rogers, Luke G.; Shanmugalingam, Nageswari; Teplyaev, Alexander 6 2020 Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates. Zbl 1441.31007Alonso-Ruiz, Patricia; Baudoin, Fabrice; Chen, Li; Rogers, Luke; Shanmugalingam, Nageswari; Teplyaev, Alexander 5 2020 Locally \(p\)-admissible measures on \(\mathbf{R}\). Zbl 1431.26012Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 3 2020 Modulus of families of sets of finte perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry. Zbl 1439.30089Jones, Rebekah; Lahti, Panu; Shanmugalingam, Nageswari 1 2020 Notions of Dirichlet problem for functions of least gradient in metric measure spaces. Zbl 1434.31008Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari 8 2019 The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property. Zbl 1429.31009Adamowicz, Tomasz; Shanmugalingam, Nageswari 3 2019 Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient. Zbl 1427.31008Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari; Speight, Gareth 2 2019 Existence and uniqueness of \(\infty \)-harmonic functions under assumption of \(\infty \)-Poincaré inequality. Zbl 1420.31003Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari 2 2019 Trace theorems for functions of bounded variation in metric spaces. Zbl 1392.26016Lahti, P.; Shanmugalingam, N. 13 2018 Trace and extension theorems for functions of bounded variation. Zbl 1406.46025Malý, Lukáš; Shanmugalingam, Nageswari; Snipes, Marie 8 2018 Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity. Zbl 1392.31014Malý, Lukáš; Shanmugalingam, Nageswari 2 2018 Dichotomy of global capacity density in metric measure spaces. Zbl 1400.49004Aikawa, Hiroaki; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 1 2018 An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability. Zbl 1391.30068Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari 1 2018 Infinity modulus and the essential metric. Zbl 1401.30065Albin, Nathan; Hoppis, Jared; Poggi-Corradini, Pietro; Shanmugalingam, Nageswari 1 2018 Fine properties and a notion of quasicontinuity for BV functions on metric spaces. Zbl 1359.30055Lahti, Panu; Shanmugalingam, Nageswari 13 2017 Geometric analysis on Cantor sets and trees. Zbl 1376.46025Björn, Anders; Björn, Jana; Gill, James T.; Shanmugalingam, Nageswari 12 2017 Characterizations of sets of finite perimeter using heat kernels in metric spaces. Zbl 1353.30054Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari 13 2016 The Mazurkiewicz distance and sets that are finitely connected at the boundary. Zbl 1342.30054Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 7 2016 Geometric characterizations of \(p\)-Poincaré inequalities in the metric setting. Zbl 1334.31007Durand-Cartagena, Estibalitz; Jaramillo, Jesus A.; Shanmugalingam, Nageswari 4 2016 Sobolev spaces on metric measure spaces. An approach based on upper gradients. Zbl 1332.46001Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 203 2015 Stability and continuity of functions of least gradient. Zbl 1318.26028Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N. 18 2015 The Dirichlet problem for \(p\)-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. Zbl 1341.31009Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 14 2015 Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces. Zbl 1307.30098Estep, Dewey; Shanmugalingam, Nageswari 10 2015 Semmes family of curves and a characterization of functions of bounded variation in terms of curves. Zbl 1327.31026Korte, Riikka; Lahti, Panu; Shanmugalingam, Nageswari 9 2015 Preservation of bounded geometry under sphericalization and flattening. Zbl 1328.30019Li, Xining; Shanmugalingam, Nageswari 9 2015 Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces. Zbl 1333.30071Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari 8 2015 Hajłasz gradients are upper gradients. Zbl 1326.46035Jiang, Renjin; Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen 6 2015 Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces. Zbl 1318.42030Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen 5 2015 A characterization of BMO self-maps of a metric measure space. Zbl 1326.30050Kinnunen, Juha; Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari 3 2015 Pointwise properties of functions of bounded variation in metric spaces. Zbl 1295.26012Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 21 2014 Intrinsic geometry and analysis of diffusion processes and \(L^{\infty}\)-variational problems. Zbl 1302.60113Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 9 2014 Geometry and analysis of Dirichlet forms. II. Zbl 1297.53033Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 8 2014 Quasiadditivity of variational capacity. Zbl 1293.31008Lehrbäck, Juha; Shanmugalingam, Nageswari 2 2014 Regularity of sets with quasiminimal boundary surfaces in metric spaces. Zbl 1311.49116Kinnunen, Juha; Korte, Riikka; Lorent, Andrew; Shanmugalingam, Nageswari 16 2013 Prime ends for domains in metric spaces. Zbl 1297.30056Adamowicz, Tomasz; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 14 2013 First order Poincaré inequalities in metric measure spaces. Zbl 1278.31012Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari 4 2013 An elementary proof of Cheeger’s theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces. Zbl 1345.31021Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari 1 2013 A characterization of Newtonian functions with zero boundary values. Zbl 1238.31008Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 21 2012 Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Zbl 1278.30026Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari 12 2012 A rigidity property of some negatively curved solvable Lie groups. Zbl 1255.22005Shanmugalingam, Nageswari; Xie, Xiangdong 10 2012 The \(\infty \)-Poincaré inequality on metric measure spaces. Zbl 1275.46018Durand-Cartagena, Estibalitz; Jaramillo, Jesús; Shanmugalingam, Nageswari 9 2012 \(p\)-Poincaré inequality versus \(\infty \)-Poincaré inequality: some counterexamples. Zbl 1255.46015Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari; Williams, Alex 6 2012 \(L^\infty\)-variational problem associated to Dirichlet forms. Zbl 1280.49028Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan 4 2012 Comparisons of relative BV-capacities and Sobolev capacity in metric spaces. Zbl 1248.28002Hakkarainen, Heikki; Shanmugalingam, Nageswari 11 2011 Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari 35 2010 Non-conformal Loewner type estimates for modulus of curve families. Zbl 1210.30020Adamowicz, Tomasz; Shanmugalingam, Nageswari 23 2010 The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces. Zbl 1211.49055Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 9 2010 Equivalence and self-improvement of \(p\)-fatness and Hardy’s inequality, and association with uniform perfectness. Zbl 1189.31006Korte, Riikka; Shanmugalingam, Nageswari 8 2010 Geometric properties of planar \(BV\)-extension domains. Zbl 1196.46025Koskela, Pekka; Miranda, Michele; Shanmugalingam, Nageswari 5 2010 Special issue: Proceedings of the ICM2010 satellite conference and international workshop on harmonic mappings and quasiconformal mappings, HQM 2010, Madras, India, August 9–17, 2010. Zbl 1229.30003 1 2010 A universality property of Sobolev spaces in metric measure spaces. Zbl 1168.46306Shanmugalingam, Nageswari 3 2009 Quasicontinuity of Newton–Sobolev functions and density of Lipschitz functions on metric spaces. Zbl 1170.46032Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 55 2008 Lebesgue points and capacities via boxing inequality in metric spaces. Zbl 1146.46018Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli 40 2008 Uniformity from Gromov hyperbolicity. Zbl 1189.30055Herron, David; Shanmugalingam, Nageswari; Xie, Xiangdong 9 2008 Maximal regularity via reverse Hölder inequalities for elliptic systems of \(n\)-Laplace type involving measures. Zbl 1158.35355Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao 1 2008 Boundary Harnack principle for \(p\)-harmonic functions in smooth Euclidean domains. Zbl 1121.35060Aikawa, Hiroaki; Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao 41 2007 Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces. Zbl 1132.46021Björn, Jana; Shanmugalingam, Nageswari 24 2007 Measurability of equivalence classes and MEC\(_p\)-property. Zbl 1146.28001Järvenpää, Esa; Järvenpää, Maarit; Rogovin, Kevin; Rogovin, Sari; Shanmugalingam, Nageswari 16 2007 Sobolev extensions of Hölder continuous and characteristic functions on metric spaces. Zbl 1137.46018Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 11 2007 Polar sets on metric spaces. Zbl 1078.31008Kinnunen, Juha; Shanmugalingam, Nageswari 14 2006 Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces. Zbl 1101.31008Juutinen, Petri; Shanmugalingam, Nageswari 7 2006 A problem of Baernstein on the equality of the \(p\)-harmonic measure of a set and its closure. Zbl 1084.31008Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 4 2006 Hölder estimates of \(p\)-harmonic extension operators. Zbl 1131.35027Aikawa, Hiroaki; Shanmugalingam, Nageswari 1 2006 Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces. Zbl 1076.31006Aikawa, Hiroaki; Shanmugalingam, Nageswari 15 2005 Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen. Zbl 1088.31005Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 16 2004 Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings. Zbl 1050.31008Shanmugalingam, Nageswari 1 2004 The Dirichlet problem for \(p\)-harmonic functions on metric spaces. Zbl 1018.31004Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 47 2003 The Perron method for \(p\)-harmonic functions in metric spaces. Zbl 1039.35033Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari 35 2003 Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces. Zbl 1027.31006Koskela, Pekka; Rajala, Kai; Shanmugalingam, Nageswari 29 2003 Some convergence results for \(p\)-harmonic functions on metric measure spaces. Zbl 1034.31006Shanmugalingam, Nageswari 25 2003 Singular functions on metric measure spaces. Zbl 1039.31016Holopainen, Ilkka; Shanmugalingam, Nageswari 16 2002 Harmonic functions on metric spaces. Zbl 0989.31003Shanmugalingam, Nageswari 109 2001 Regularity of quasi-minimizers on metric spaces. Zbl 1006.49027Kinnunen, Juha; Shanmugalingam, Nageswari 105 2001 Sobolev classes of Banach space-valued functions and quasiconformal mappings. Zbl 1013.46023Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 77 2001 Fat sets and pointwise boundary estimates for \(p\)-harmonic functions in metric spaces. Zbl 1003.31004Björn, Jana; MacManus, Paul; Shanmugalingam, Nageswari 37 2001 Modulus and continuous capacity. Zbl 1002.31004Kallunki, Sari; Shanmugalingam, Nageswari 28 2001 On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T. 4 2001 Newtonian spaces: An extension of Sobolev spaces to metric measure spaces. Zbl 0974.46038Shanmugalingam, Nageswari 307 2000 Removable sets for the Poincaré inequality on metric spaces. Zbl 0958.30008Koskela, P.; Shanmugalingam, N.; Tuominen, H. 9 2000 all cited Publications top 5 cited Publications all top 5 Cited by 607 Authors 63 Shanmugalingam, Nageswari 41 Björn, Anders 38 Björn, Jana 30 Lahti, Panu 22 Kinnunen, Juha 21 Gigli, Nicola 21 Koskela, Pekka 21 Yang, Dachun 20 Korte, Riikka 17 Sevost’yanov, Yevgen Oleksandrovych 16 Tuominen, Heli 13 Ambrosio, Luigi 12 Jiang, Renjin 12 Lehrbäck, Juha 12 Marola, Niko 12 Yuan, Wen 11 Górka, Przemysław 11 Pasqualetto, Enrico 11 Wenger, Stefan 10 Heikkinen, Toni 10 Zhou, Yuan 9 Adamowicz, Tomasz 9 Honda, Shouhei 9 Martio, Olli 9 Savaré, Giuseppe 9 Soultanis, Elefterios 8 Eriksson-Bique, Sylvester 8 Hajłasz, Piotr 8 Lytchak, Alexander 7 Miranda, Michele jun. 7 Tyson, Jeremy T. 7 Wang, Zhuang 7 Zhang, Huichun 6 Aikawa, Hiroaki 6 Di Marino, Simone 6 Górny, Wojciech 6 Guo, Changyu 6 Heinonen, Juha 6 Kuusi, Tuomo 6 Latvala, Visa 6 Manfredi, Juan J. 6 Parviainen, Mikko 6 Speight, Gareth 6 Vähäkangas, Antti V. 6 Xie, Xiangdong 6 Zürcher, Thomas 5 Aldaz, Jésus Munárriz 5 Anza Hafsa, Omar 5 Baudoin, Fabrice 5 Durand-Cartagena, Estibalitz 5 Hakkarainen, Heikki 5 Jaramillo, Jesús Angel 5 Li, Xining 5 Li, Yaxiang 5 Mandallena, Jean-Philippe 5 Masson, Mathias 5 Nyström, Kaj 5 Rajala, Tapio 5 Teplyaev, Alexander 5 Wildrick, Kevin 5 Zhou, Qingshan 4 Alonso-Ruiz, Patricia 4 Buffa, Vito 4 Gogatishvili, Amiran 4 Hansevi, Daniel 4 Hirata, Kentaro 4 Huang, Jiacheng 4 Huang, Xiaojun 4 Il’yutko, Denis Petrovich 4 Karak, Nijjwal 4 Liu, Yu 4 Maldonado, Diego 4 Malý, Lukáš 4 Mondino, Andrea 4 Pinamonti, Andrea 4 Pratelli, Aldo 4 Rajala, Kai 4 Rogers, Luke G. 4 Siljander, Juhana 4 Song, Renming 4 Williams, Marshall 3 Antonelli, Gioacchino 3 Balogh, Zoltán M. 3 Bogdan, Krzysztof 3 Bögelein, Verena 3 Bonk, Mario 3 Ciska-Niedziałomska, Małgorzata 3 Comi, Giovanni E. 3 Del Pezzo, Leandro M. 3 Duzaar, Frank 3 Fässler, Katrin S. 3 Fusco, Nicola 3 Gaczkowski, Michał 3 Garofalo, Nicola 3 Gill, James T. 3 Gol’dshtein, Vladimir Mikhailovich 3 Gong, Jasun 3 Han, Bangxian 3 Ikonen, Toni 3 Kim, Panki ...and 507 more Authors all top 5 Cited in 151 Serials 40 Journal of Mathematical Analysis and Applications 38 Calculus of Variations and Partial Differential Equations 36 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Potential Analysis 32 Journal of Functional Analysis 23 The Journal of Geometric Analysis 20 Proceedings of the American Mathematical Society 20 Analysis and Geometry in Metric Spaces 19 Mathematische Zeitschrift 18 Annales Academiae Scientiarum Fennicae. Mathematica 17 Mathematische Annalen 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Journal of Differential Equations 15 Revista Matemática Iberoamericana 14 Transactions of the American Mathematical Society 13 Advances in Mathematics 13 Annales Fennici Mathematici 12 Journal d’Analyse Mathématique 12 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Manuscripta Mathematica 7 Michigan Mathematical Journal 7 Journal of Mathematical Sciences (New York) 7 Advances in Calculus of Variations 6 Collectanea Mathematica 6 Duke Mathematical Journal 6 Illinois Journal of Mathematics 6 Communications in Contemporary Mathematics 5 Archive for Rational Mechanics and Analysis 5 Archiv der Mathematik 5 Indiana University Mathematics Journal 5 Journal für die Reine und Angewandte Mathematik 5 Geometric and Functional Analysis. GAFA 5 Conformal Geometry and Dynamics 5 Revista Matemática Complutense 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 5 Complex Variables and Elliptic Equations 5 Analysis and Mathematical Physics 4 Ukrainian Mathematical Journal 4 Arkiv för Matematik 4 Journal of the Mathematical Society of Japan 4 Memoirs of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Forum Mathematicum 4 SIAM Journal on Mathematical Analysis 4 Bulletin des Sciences Mathématiques 4 Geometry & Topology 4 Science China. Mathematics 3 Communications on Pure and Applied Mathematics 3 Studia Mathematica 3 The Annals of Probability 3 Geometriae Dedicata 3 Inventiones Mathematicae 3 Ricerche di Matematica 3 Tohoku Mathematical Journal. Second Series 3 Expositiones Mathematicae 3 St. Petersburg Mathematical Journal 3 Positivity 3 Lobachevskii Journal of Mathematics 3 Journal of Fixed Point Theory and Applications 3 Journal of Function Spaces 2 Mathematical Notes 2 Annales de l’Institut Fourier 2 Canadian Mathematical Bulletin 2 Czechoslovak Mathematical Journal 2 Mathematische Nachrichten 2 Probability Theory and Related Fields 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Communications in Partial Differential Equations 2 NoDEA. Nonlinear Differential Equations and Applications 2 Sbornik: Mathematics 2 The Journal of Fourier Analysis and Applications 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Journal of the Australian Mathematical Society 2 Advanced Nonlinear Studies 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Complex Analysis and Operator Theory 2 Frontiers of Mathematics in China 2 Discrete and Continuous Dynamical Systems. Series S 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Bulletin of Mathematical Sciences 2 Complex Analysis and its Synergies 1 Bulletin of the Australian Mathematical Society 1 Israel Journal of Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 American Journal of Mathematics 1 Annales Polonici Mathematici 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Commentarii Mathematici Helvetici 1 Demonstratio Mathematica 1 Publications Mathématiques 1 Integral Equations and Operator Theory 1 Journal of Differential Geometry 1 Kodai Mathematical Journal 1 Mathematica Scandinavica 1 Monatshefte für Mathematik 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University ...and 51 more Serials all top 5 Cited in 42 Fields 236 Functions of a complex variable (30-XX) 214 Functional analysis (46-XX) 176 Potential theory (31-XX) 175 Partial differential equations (35-XX) 134 Differential geometry (53-XX) 107 Calculus of variations and optimal control; optimization (49-XX) 81 Real functions (26-XX) 77 Measure and integration (28-XX) 67 Global analysis, analysis on manifolds (58-XX) 64 Harmonic analysis on Euclidean spaces (42-XX) 34 Operator theory (47-XX) 32 Probability theory and stochastic processes (60-XX) 26 General topology (54-XX) 23 Topological groups, Lie groups (22-XX) 21 Abstract harmonic analysis (43-XX) 10 Group theory and generalizations (20-XX) 10 Geometry (51-XX) 8 Combinatorics (05-XX) 7 Convex and discrete geometry (52-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Difference and functional equations (39-XX) 4 Manifolds and cell complexes (57-XX) 3 Ordinary differential equations (34-XX) 3 Quantum theory (81-XX) 2 Algebraic geometry (14-XX) 2 Integral equations (45-XX) 2 Algebraic topology (55-XX) 2 Statistics (62-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Approximations and expansions (41-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year