## Shanmugalingam, Nageswari

Compute Distance To:
 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
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### 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
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### 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
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### 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)

### 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 0974.46038
Shanmugalingam, Nageswari
2000
Sobolev spaces on metric measure spaces. An approach based on upper gradients. Zbl 1332.46001
Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2015
Harmonic functions on metric spaces. Zbl 0989.31003
Shanmugalingam, Nageswari
2001
Regularity of quasi-minimizers on metric spaces. Zbl 1006.49027
Kinnunen, Juha; Shanmugalingam, Nageswari
2001
Sobolev classes of Banach space-valued functions and quasiconformal mappings. Zbl 1013.46023
Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
Quasicontinuity of Newton–Sobolev functions and density of Lipschitz functions on metric spaces. Zbl 1170.46032
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2008
The Dirichlet problem for $$p$$-harmonic functions on metric spaces. Zbl 1018.31004
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2003
Boundary Harnack principle for $$p$$-harmonic functions in smooth Euclidean domains. Zbl 1121.35060
Aikawa, Hiroaki; Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao
2007
Lebesgue points and capacities via boxing inequality in metric spaces. Zbl 1146.46018
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2008
Fat sets and pointwise boundary estimates for $$p$$-harmonic functions in metric spaces. Zbl 1003.31004
Björn, Jana; MacManus, Paul; Shanmugalingam, Nageswari
2001
The Perron method for $$p$$-harmonic functions in metric spaces. Zbl 1039.35033
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2003
Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033
Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari
2010
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces. Zbl 1027.31006
Koskela, Pekka; Rajala, Kai; Shanmugalingam, Nageswari
2003
Modulus and continuous capacity. Zbl 1002.31004
Kallunki, Sari; Shanmugalingam, Nageswari
2001
Some convergence results for $$p$$-harmonic functions on metric measure spaces. Zbl 1034.31006
Shanmugalingam, Nageswari
2003
Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces. Zbl 1132.46021
Björn, Jana; Shanmugalingam, Nageswari
2007
Non-conformal Loewner type estimates for modulus of curve families. Zbl 1210.30020
2010
Pointwise properties of functions of bounded variation in metric spaces. Zbl 1295.26012
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2014
A characterization of Newtonian functions with zero boundary values. Zbl 1238.31008
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2012
Stability and continuity of functions of least gradient. Zbl 1318.26028
Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N.
2015
Singular functions on metric measure spaces. Zbl 1039.31016
Holopainen, Ilkka; Shanmugalingam, Nageswari
2002
Measurability of equivalence classes and MEC$$_p$$-property. Zbl 1146.28001
Järvenpää, Esa; Järvenpää, Maarit; Rogovin, Kevin; Rogovin, Sari; Shanmugalingam, Nageswari
2007
Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen. Zbl 1088.31005
Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2004
Regularity of sets with quasiminimal boundary surfaces in metric spaces. Zbl 1311.49116
Kinnunen, Juha; Korte, Riikka; Lorent, Andrew; Shanmugalingam, Nageswari
2013
Carleson type estimates for $$p$$-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces. Zbl 1076.31006
Aikawa, Hiroaki; Shanmugalingam, Nageswari
2005
The Dirichlet problem for $$p$$-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. Zbl 1341.31009
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2015
Polar sets on metric spaces. Zbl 1078.31008
Kinnunen, Juha; Shanmugalingam, Nageswari
2006
Prime ends for domains in metric spaces. Zbl 1297.30056
Adamowicz, Tomasz; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2013
Fine properties and a notion of quasicontinuity for BV functions on metric spaces. Zbl 1359.30055
Lahti, Panu; Shanmugalingam, Nageswari
2017
Trace theorems for functions of bounded variation in metric spaces. Zbl 1392.26016
Lahti, P.; Shanmugalingam, N.
2018
Characterizations of sets of finite perimeter using heat kernels in metric spaces. Zbl 1353.30054
Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari
2016
Geometric analysis on Cantor sets and trees. Zbl 1376.46025
Björn, Anders; Björn, Jana; Gill, James T.; Shanmugalingam, Nageswari
2017
Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Zbl 1278.30026
Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari
2012
Sobolev extensions of Hölder continuous and characteristic functions on metric spaces. Zbl 1137.46018
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2007
Comparisons of relative BV-capacities and Sobolev capacity in metric spaces. Zbl 1248.28002
Hakkarainen, Heikki; Shanmugalingam, Nageswari
2011
Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces. Zbl 1307.30098
Estep, Dewey; Shanmugalingam, Nageswari
2015
A rigidity property of some negatively curved solvable Lie groups. Zbl 1255.22005
Shanmugalingam, Nageswari; Xie, Xiangdong
2012
Removable sets for the Poincaré inequality on metric spaces. Zbl 0958.30008
Koskela, P.; Shanmugalingam, N.; Tuominen, H.
2000
The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces. Zbl 1211.49055
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2010
Intrinsic geometry and analysis of diffusion processes and $$L^{\infty}$$-variational problems. Zbl 1302.60113
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2014
Uniformity from Gromov hyperbolicity. Zbl 1189.30055
Herron, David; Shanmugalingam, Nageswari; Xie, Xiangdong
2008
The $$\infty$$-Poincaré inequality on metric measure spaces. Zbl 1275.46018
Durand-Cartagena, Estibalitz; Jaramillo, Jesús; Shanmugalingam, Nageswari
2012
Semmes family of curves and a characterization of functions of bounded variation in terms of curves. Zbl 1327.31026
Korte, Riikka; Lahti, Panu; Shanmugalingam, Nageswari
2015
Preservation of bounded geometry under sphericalization and flattening. Zbl 1328.30019
Li, Xining; Shanmugalingam, Nageswari
2015
Geometry and analysis of Dirichlet forms. II. Zbl 1297.53033
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2014
Trace and extension theorems for functions of bounded variation. Zbl 1406.46025
Malý, Lukáš; Shanmugalingam, Nageswari; Snipes, Marie
2018
Equivalence and self-improvement of $$p$$-fatness and Hardy’s inequality, and association with uniform perfectness. Zbl 1189.31006
Korte, Riikka; Shanmugalingam, Nageswari
2010
Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces. Zbl 1333.30071
Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari
2015
Notions of Dirichlet problem for functions of least gradient in metric measure spaces. Zbl 1434.31008
Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari
2019
Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces. Zbl 1101.31008
Juutinen, Petri; Shanmugalingam, Nageswari
2006
The Mazurkiewicz distance and sets that are finitely connected at the boundary. Zbl 1342.30054
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2016
Jiang, Renjin; Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen
2015
$$p$$-Poincaré inequality versus $$\infty$$-Poincaré inequality: some counterexamples. Zbl 1255.46015
Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari; Williams, Alex
2012
Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities. Zbl 07179616
Ruiz, Patricia Alonso; Baudoin, Fabrice; Chen, Li; Rogers, Luke G.; Shanmugalingam, Nageswari; Teplyaev, Alexander
2020
Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces. Zbl 1318.42030
Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen
2015
Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates. Zbl 1441.31007
Alonso-Ruiz, Patricia; Baudoin, Fabrice; Chen, Li; Rogers, Luke; Shanmugalingam, Nageswari; Teplyaev, Alexander
2020
Geometric properties of planar $$BV$$-extension domains. Zbl 1196.46025
Koskela, Pekka; Miranda, Michele; Shanmugalingam, Nageswari
2010
The Liouville theorem for $$p$$-harmonic functions and quasiminimizers with finite energy. Zbl 1456.35055
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2021
Geometric characterizations of $$p$$-Poincaré inequalities in the metric setting. Zbl 1334.31007
Durand-Cartagena, Estibalitz; Jaramillo, Jesus A.; Shanmugalingam, Nageswari
2016
On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006
Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
A problem of Baernstein on the equality of the $$p$$-harmonic measure of a set and its closure. Zbl 1084.31008
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2006
First order Poincaré inequalities in metric measure spaces. Zbl 1278.31012
Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari
2013
$$L^\infty$$-variational problem associated to Dirichlet forms. Zbl 1280.49028
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2012
Bounded geometry and $$p$$-harmonic functions under uniformization and hyperbolization. Zbl 1466.53048
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2021
A universality property of Sobolev spaces in metric measure spaces. Zbl 1168.46306
Shanmugalingam, Nageswari
2009
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property. Zbl 1429.31009
2019
Locally $$p$$-admissible measures on $$\mathbf{R}$$. Zbl 1431.26012
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2020
A characterization of BMO self-maps of a metric measure space. Zbl 1326.30050
Kinnunen, Juha; Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari
2015
Quasiadditivity of variational capacity. Zbl 1293.31008
Lehrbäck, Juha; Shanmugalingam, Nageswari
2014
Neumann problem for $$p$$-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity. Zbl 1392.31014
Malý, Lukáš; Shanmugalingam, Nageswari
2018
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient. Zbl 1427.31008
Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari; Speight, Gareth
2019
Existence and uniqueness of $$\infty$$-harmonic functions under assumption of $$\infty$$-Poincaré inequality. Zbl 1420.31003
Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari
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 1480.46042
Lindquist, Jeff; Shanmugalingam, Nageswari
2021
Maximal regularity via reverse Hölder inequalities for elliptic systems of $$n$$-Laplace type involving measures. Zbl 1158.35355
Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao
2008
Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings. Zbl 1050.31008
Shanmugalingam, Nageswari
2004
Hölder estimates of $$p$$-harmonic extension operators. Zbl 1131.35027
Aikawa, Hiroaki; Shanmugalingam, Nageswari
2006
Modulus of families of sets of finte perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry. Zbl 1439.30089
Jones, Rebekah; Lahti, Panu; Shanmugalingam, Nageswari
2020
Dichotomy of global capacity density in metric measure spaces. Zbl 1400.49004
Aikawa, Hiroaki; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2018
An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability. Zbl 1391.30068
Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari
2018
Infinity modulus and the essential metric. Zbl 1401.30065
Albin, Nathan; Hoppis, Jared; Poggi-Corradini, Pietro; Shanmugalingam, Nageswari
2018
An elementary proof of Cheeger’s theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces. Zbl 1345.31021
Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari
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
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 1480.26004
Durand-Cartagena, Estibalitz; Eriksson-Bique, Sylvester; Korte, Riikka; Shanmugalingam, Nageswari
2021
Rough isometry between Gromov hyperbolic spaces and uniformization. Zbl 1477.53074
Lindquist, Jeff; Shanmugalingam, Nageswari
2021
Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry. Zbl 1477.30056
Eriksson-Bique, Sylvester; Giovannardi, Gianmarco; Korte, Riikka; Shanmugalingam, Nageswari; Speight, Gareth
2022
Extension and trace results for doubling metric measure spaces and their hyperbolic fillings. Zbl 07485591
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2022
Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry. Zbl 1477.30056
Eriksson-Bique, Sylvester; Giovannardi, Gianmarco; Korte, Riikka; Shanmugalingam, Nageswari; Speight, Gareth
2022
Extension and trace results for doubling metric measure spaces and their hyperbolic fillings. Zbl 07485591
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2022
The Liouville theorem for $$p$$-harmonic functions and quasiminimizers with finite energy. Zbl 1456.35055
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2021
Bounded geometry and $$p$$-harmonic functions under uniformization and hyperbolization. Zbl 1466.53048
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
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 1480.46042
Lindquist, Jeff; Shanmugalingam, Nageswari
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 1480.26004
Durand-Cartagena, Estibalitz; Eriksson-Bique, Sylvester; Korte, Riikka; Shanmugalingam, Nageswari
2021
Rough isometry between Gromov hyperbolic spaces and uniformization. Zbl 1477.53074
Lindquist, Jeff; Shanmugalingam, Nageswari
2021
Besov class via heat semigroup on Dirichlet spaces. I: Sobolev type inequalities. Zbl 07179616
Ruiz, Patricia Alonso; Baudoin, Fabrice; Chen, Li; Rogers, Luke G.; Shanmugalingam, Nageswari; Teplyaev, Alexander
2020
Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates. Zbl 1441.31007
Alonso-Ruiz, Patricia; Baudoin, Fabrice; Chen, Li; Rogers, Luke; Shanmugalingam, Nageswari; Teplyaev, Alexander
2020
Locally $$p$$-admissible measures on $$\mathbf{R}$$. Zbl 1431.26012
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2020
Modulus of families of sets of finte perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry. Zbl 1439.30089
Jones, Rebekah; Lahti, Panu; Shanmugalingam, Nageswari
2020
Notions of Dirichlet problem for functions of least gradient in metric measure spaces. Zbl 1434.31008
Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari
2019
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property. Zbl 1429.31009
2019
Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient. Zbl 1427.31008
Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari; Speight, Gareth
2019
Existence and uniqueness of $$\infty$$-harmonic functions under assumption of $$\infty$$-Poincaré inequality. Zbl 1420.31003
Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari
2019
Trace theorems for functions of bounded variation in metric spaces. Zbl 1392.26016
Lahti, P.; Shanmugalingam, N.
2018
Trace and extension theorems for functions of bounded variation. Zbl 1406.46025
Malý, Lukáš; Shanmugalingam, Nageswari; Snipes, Marie
2018
Neumann problem for $$p$$-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity. Zbl 1392.31014
Malý, Lukáš; Shanmugalingam, Nageswari
2018
Dichotomy of global capacity density in metric measure spaces. Zbl 1400.49004
Aikawa, Hiroaki; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2018
An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability. Zbl 1391.30068
Lahti, Panu; Malý, Lukáš; Shanmugalingam, Nageswari
2018
Infinity modulus and the essential metric. Zbl 1401.30065
Albin, Nathan; Hoppis, Jared; Poggi-Corradini, Pietro; Shanmugalingam, Nageswari
2018
Fine properties and a notion of quasicontinuity for BV functions on metric spaces. Zbl 1359.30055
Lahti, Panu; Shanmugalingam, Nageswari
2017
Geometric analysis on Cantor sets and trees. Zbl 1376.46025
Björn, Anders; Björn, Jana; Gill, James T.; Shanmugalingam, Nageswari
2017
Characterizations of sets of finite perimeter using heat kernels in metric spaces. Zbl 1353.30054
Marola, Niko; Miranda, Michele&nbsp;jun.; Shanmugalingam, Nageswari
2016
The Mazurkiewicz distance and sets that are finitely connected at the boundary. Zbl 1342.30054
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2016
Geometric characterizations of $$p$$-Poincaré inequalities in the metric setting. Zbl 1334.31007
Durand-Cartagena, Estibalitz; Jaramillo, Jesus A.; Shanmugalingam, Nageswari
2016
Sobolev spaces on metric measure spaces. An approach based on upper gradients. Zbl 1332.46001
Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2015
Stability and continuity of functions of least gradient. Zbl 1318.26028
Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N.
2015
The Dirichlet problem for $$p$$-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. Zbl 1341.31009
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2015
Geometry of prime end boundary and the Dirichlet problem for bounded domains in metric measure spaces. Zbl 1307.30098
Estep, Dewey; Shanmugalingam, Nageswari
2015
Semmes family of curves and a characterization of functions of bounded variation in terms of curves. Zbl 1327.31026
Korte, Riikka; Lahti, Panu; Shanmugalingam, Nageswari
2015
Preservation of bounded geometry under sphericalization and flattening. Zbl 1328.30019
Li, Xining; Shanmugalingam, Nageswari
2015
Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces. Zbl 1333.30071
Marola, Niko; Miranda, Michele jun.; Shanmugalingam, Nageswari
2015
Jiang, Renjin; Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen
2015
Newton-Besov spaces and Newton-Triebel-Lizorkin spaces on metric measure spaces. Zbl 1318.42030
Shanmugalingam, Nageswari; Yang, Dachun; Yuan, Wen
2015
A characterization of BMO self-maps of a metric measure space. Zbl 1326.30050
Kinnunen, Juha; Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari
2015
Pointwise properties of functions of bounded variation in metric spaces. Zbl 1295.26012
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2014
Intrinsic geometry and analysis of diffusion processes and $$L^{\infty}$$-variational problems. Zbl 1302.60113
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2014
Geometry and analysis of Dirichlet forms. II. Zbl 1297.53033
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2014
Quasiadditivity of variational capacity. Zbl 1293.31008
Lehrbäck, Juha; Shanmugalingam, Nageswari
2014
Regularity of sets with quasiminimal boundary surfaces in metric spaces. Zbl 1311.49116
Kinnunen, Juha; Korte, Riikka; Lorent, Andrew; Shanmugalingam, Nageswari
2013
Prime ends for domains in metric spaces. Zbl 1297.30056
Adamowicz, Tomasz; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2013
First order Poincaré inequalities in metric measure spaces. Zbl 1278.31012
Durand-Cartagena, Estibalitz; Jaramillo, Jesús A.; Shanmugalingam, Nageswari
2013
An elementary proof of Cheeger’s theorem on reflexivity of Newton-Sobolev spaces of functions in metric measure spaces. Zbl 1345.31021
Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari
2013
A characterization of Newtonian functions with zero boundary values. Zbl 1238.31008
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2012
Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Zbl 1278.30026
Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari
2012
A rigidity property of some negatively curved solvable Lie groups. Zbl 1255.22005
Shanmugalingam, Nageswari; Xie, Xiangdong
2012
The $$\infty$$-Poincaré inequality on metric measure spaces. Zbl 1275.46018
Durand-Cartagena, Estibalitz; Jaramillo, Jesús; Shanmugalingam, Nageswari
2012
$$p$$-Poincaré inequality versus $$\infty$$-Poincaré inequality: some counterexamples. Zbl 1255.46015
Durand-Cartagena, Estibalitz; Shanmugalingam, Nageswari; Williams, Alex
2012
$$L^\infty$$-variational problem associated to Dirichlet forms. Zbl 1280.49028
Koskela, Pekka; Shanmugalingam, Nageswari; Zhou, Yuan
2012
Comparisons of relative BV-capacities and Sobolev capacity in metric spaces. Zbl 1248.28002
Hakkarainen, Heikki; Shanmugalingam, Nageswari
2011
Interpolation properties of Besov spaces defined on metric spaces. Zbl 1195.46033
Gogatishvili, Amiran; Koskela, Pekka; Shanmugalingam, Nageswari
2010
Non-conformal Loewner type estimates for modulus of curve families. Zbl 1210.30020
2010
The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces. Zbl 1211.49055
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2010
Equivalence and self-improvement of $$p$$-fatness and Hardy’s inequality, and association with uniform perfectness. Zbl 1189.31006
Korte, Riikka; Shanmugalingam, Nageswari
2010
Geometric properties of planar $$BV$$-extension domains. Zbl 1196.46025
Koskela, Pekka; Miranda, Michele; Shanmugalingam, Nageswari
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
2010
A universality property of Sobolev spaces in metric measure spaces. Zbl 1168.46306
Shanmugalingam, Nageswari
2009
Quasicontinuity of Newton–Sobolev functions and density of Lipschitz functions on metric spaces. Zbl 1170.46032
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2008
Lebesgue points and capacities via boxing inequality in metric spaces. Zbl 1146.46018
Kinnunen, Juha; Korte, Riikka; Shanmugalingam, Nageswari; Tuominen, Heli
2008
Uniformity from Gromov hyperbolicity. Zbl 1189.30055
Herron, David; Shanmugalingam, Nageswari; Xie, Xiangdong
2008
Maximal regularity via reverse Hölder inequalities for elliptic systems of $$n$$-Laplace type involving measures. Zbl 1158.35355
Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao
2008
Boundary Harnack principle for $$p$$-harmonic functions in smooth Euclidean domains. Zbl 1121.35060
Aikawa, Hiroaki; Kilpeläinen, Tero; Shanmugalingam, Nageswari; Zhong, Xiao
2007
Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces. Zbl 1132.46021
Björn, Jana; Shanmugalingam, Nageswari
2007
Measurability of equivalence classes and MEC$$_p$$-property. Zbl 1146.28001
Järvenpää, Esa; Järvenpää, Maarit; Rogovin, Kevin; Rogovin, Sari; Shanmugalingam, Nageswari
2007
Sobolev extensions of Hölder continuous and characteristic functions on metric spaces. Zbl 1137.46018
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2007
Polar sets on metric spaces. Zbl 1078.31008
Kinnunen, Juha; Shanmugalingam, Nageswari
2006
Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces. Zbl 1101.31008
Juutinen, Petri; Shanmugalingam, Nageswari
2006
A problem of Baernstein on the equality of the $$p$$-harmonic measure of a set and its closure. Zbl 1084.31008
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2006
Hölder estimates of $$p$$-harmonic extension operators. Zbl 1131.35027
Aikawa, Hiroaki; Shanmugalingam, Nageswari
2006
Carleson type estimates for $$p$$-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces. Zbl 1076.31006
Aikawa, Hiroaki; Shanmugalingam, Nageswari
2005
Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen. Zbl 1088.31005
Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2004
Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings. Zbl 1050.31008
Shanmugalingam, Nageswari
2004
The Dirichlet problem for $$p$$-harmonic functions on metric spaces. Zbl 1018.31004
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2003
The Perron method for $$p$$-harmonic functions in metric spaces. Zbl 1039.35033
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari
2003
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces. Zbl 1027.31006
Koskela, Pekka; Rajala, Kai; Shanmugalingam, Nageswari
2003
Some convergence results for $$p$$-harmonic functions on metric measure spaces. Zbl 1034.31006
Shanmugalingam, Nageswari
2003
Singular functions on metric measure spaces. Zbl 1039.31016
Holopainen, Ilkka; Shanmugalingam, Nageswari
2002
Harmonic functions on metric spaces. Zbl 0989.31003
Shanmugalingam, Nageswari
2001
Regularity of quasi-minimizers on metric spaces. Zbl 1006.49027
Kinnunen, Juha; Shanmugalingam, Nageswari
2001
Sobolev classes of Banach space-valued functions and quasiconformal mappings. Zbl 1013.46023
Heinonen, Juha; Koskela, Pekka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
Fat sets and pointwise boundary estimates for $$p$$-harmonic functions in metric spaces. Zbl 1003.31004
Björn, Jana; MacManus, Paul; Shanmugalingam, Nageswari
2001
Modulus and continuous capacity. Zbl 1002.31004
Kallunki, Sari; Shanmugalingam, Nageswari
2001
On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006
Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
Newtonian spaces: An extension of Sobolev spaces to metric measure spaces. Zbl 0974.46038
Shanmugalingam, Nageswari
2000
Removable sets for the Poincaré inequality on metric spaces. Zbl 0958.30008
Koskela, P.; Shanmugalingam, N.; Tuominen, H.
2000
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### 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
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### 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
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### 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)