Colbois, Bruno; Girouard, Alexandre; Gordon, Carolyn; Sher, David Some recent developments on the Steklov eigenvalue problem. (English) Zbl 07800518 Rev. Mat. Complut. 37, No. 1, 1-161 (2024). Reviewer: Emilio A. Lauret (Bahía Blanca) MSC: 58C40 58J50 35P05 35P15 35P20 35P30 53A10 53C21 58J53 58-02 53-02 PDFBibTeX XMLCite \textit{B. Colbois} et al., Rev. Mat. Complut. 37, No. 1, 1--161 (2024; Zbl 07800518) Full Text: DOI arXiv OA License
Petrides, Romain Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids. (English) Zbl 1523.53063 J. Funct. Anal. 285, No. 10, Article ID 110087, 75 p. (2023). Reviewer: Emilio A. Lauret (Bahía Blanca) MSC: 53C42 58J50 PDFBibTeX XMLCite \textit{R. Petrides}, J. Funct. Anal. 285, No. 10, Article ID 110087, 75 p. (2023; Zbl 1523.53063) Full Text: DOI
Ros, Antonio On the first eigenvalue of the Laplacian on compact surfaces of genus three. (English) Zbl 1496.35268 J. Math. Soc. Japan 74, No. 3, 813-828 (2022). MSC: 35P15 35J05 53A10 58C40 58J05 58J50 PDFBibTeX XMLCite \textit{A. Ros}, J. Math. Soc. Japan 74, No. 3, 813--828 (2022; Zbl 1496.35268) Full Text: DOI arXiv
Matthiesen, Henrik; Siffert, Anna Existence of metrics maximizing the first eigenvalue on non-orientable surfaces. (English) Zbl 1484.35301 J. Spectr. Theory 11, No. 3, 1279-1296 (2021). MSC: 35P15 49Q05 49Q10 58E11 58E20 58J05 PDFBibTeX XMLCite \textit{H. Matthiesen} and \textit{A. Siffert}, J. Spectr. Theory 11, No. 3, 1279--1296 (2021; Zbl 1484.35301) Full Text: DOI arXiv
Girouard, Alexandre; Lagacé, Jean Large Steklov eigenvalues via homogenisation on manifolds. (English) Zbl 1477.58019 Invent. Math. 226, No. 3, 1011-1056 (2021). MSC: 58J50 35P15 53C42 PDFBibTeX XMLCite \textit{A. Girouard} and \textit{J. Lagacé}, Invent. Math. 226, No. 3, 1011--1056 (2021; Zbl 1477.58019) Full Text: DOI arXiv
Karpukhin, Mikhail; Nadirashvili, Nikolai; Penskoi, Alexei V.; Polterovich, Iosif An isoperimetric inequality for Laplace eigenvalues on the sphere. (English) Zbl 1471.53056 J. Differ. Geom. 118, No. 2, 313-333 (2021). Reviewer: Mohammed El Aïdi (Bogotá) MSC: 53C42 58E11 58J50 PDFBibTeX XMLCite \textit{M. Karpukhin} et al., J. Differ. Geom. 118, No. 2, 313--333 (2021; Zbl 1471.53056) Full Text: DOI arXiv
Lohi, Jonni; Kettunen, Lauri Whitney forms and their extensions. (English) Zbl 1468.65200 J. Comput. Appl. Math. 393, Article ID 113520, 19 p. (2021). MSC: 65N30 58A10 PDFBibTeX XMLCite \textit{J. Lohi} and \textit{L. Kettunen}, J. Comput. Appl. Math. 393, Article ID 113520, 19 p. (2021; Zbl 1468.65200) Full Text: DOI
Karpukhin, Mikhail Index of minimal spheres and isoperimetric eigenvalue inequalities. (English) Zbl 1503.53122 Invent. Math. 223, No. 1, 335-377 (2021). MSC: 53C42 58J20 53C28 PDFBibTeX XMLCite \textit{M. Karpukhin}, Invent. Math. 223, No. 1, 335--377 (2021; Zbl 1503.53122) Full Text: DOI arXiv
Penskoi, Alexei V. Isoperimetric inequalities for higher eigenvalues of the Laplace-Beltrami operator on surfaces. (English. Russian original) Zbl 1434.58012 Proc. Steklov Inst. Math. 305, 270-286 (2019); translation from Tr. Mat. Inst. Steklova 305, 291-308 (2019). Reviewer: Emilio A. Lauret (Bahía Blanca) MSC: 58J50 PDFBibTeX XMLCite \textit{A. V. Penskoi}, Proc. Steklov Inst. Math. 305, 270--286 (2019; Zbl 1434.58012); translation from Tr. Mat. Inst. Steklova 305, 291--308 (2019) Full Text: DOI
Karpukhin, Mikhail On the Yang-Yau inequality for the first Laplace eigenvalue. (English) Zbl 1429.58040 Geom. Funct. Anal. 29, No. 6, 1864-1885 (2019). MSC: 58J50 53A10 58E20 PDFBibTeX XMLCite \textit{M. Karpukhin}, Geom. Funct. Anal. 29, No. 6, 1864--1885 (2019; Zbl 1429.58040) Full Text: DOI arXiv
Cianci, Donato; Karpukhin, Mikhail; Medvedev, Vladimir On branched minimal immersions of surfaces by first eigenfunctions. (English) Zbl 1427.53080 Ann. Global Anal. Geom. 56, No. 4, 667-690 (2019). MSC: 53C42 58J50 PDFBibTeX XMLCite \textit{D. Cianci} et al., Ann. Global Anal. Geom. 56, No. 4, 667--690 (2019; Zbl 1427.53080) Full Text: DOI arXiv
Nayatani, Shin; Shoda, Toshihiro Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian. (Métriques sur une surface fermée de genre deux qui maximisent la première valeur propre du laplacien.) (English. French summary) Zbl 1408.58023 C. R., Math., Acad. Sci. Paris 357, No. 1, 84-98 (2019). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 35P15 PDFBibTeX XMLCite \textit{S. Nayatani} and \textit{T. Shoda}, C. R., Math., Acad. Sci. Paris 357, No. 1, 84--98 (2019; Zbl 1408.58023) Full Text: DOI arXiv
Gerhards, Christian Spherical potential theory: tools and applications. (English) Zbl 1414.35055 Freeden, Willi (ed.) et al., Handbook of mathematical geodesy. Functional analytic and potential theoretic methods. Cham: Birkhäuser. Geosyst. Math., 821-853 (2018). MSC: 35J05 58J05 35A01 PDFBibTeX XMLCite \textit{C. Gerhards}, in: Handbook of mathematical geodesy. Functional analytic and potential theoretic methods. Cham: Birkhäuser. 821--853 (2018; Zbl 1414.35055) Full Text: DOI arXiv
Le Gia, Quoc T. Numerical solutions of a boundary value problem on the sphere using radial basis functions. (English) Zbl 1407.65309 Dick, Josef (ed.) et al., Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Cham: Springer. 815-836 (2018). MSC: 65N35 58J32 35Q86 86A05 PDFBibTeX XMLCite \textit{Q. T. Le Gia}, in: Contemporary computational mathematics -- a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Cham: Springer. 815--836 (2018; Zbl 1407.65309) Full Text: DOI arXiv
O’Neil, Michael Second-kind integral equations for the Laplace-Beltrami problem on surfaces in three dimensions. (English) Zbl 1404.35121 Adv. Comput. Math. 44, No. 5, 1385-1409 (2018). MSC: 35J05 58J05 31C12 PDFBibTeX XMLCite \textit{M. O'Neil}, Adv. Comput. Math. 44, No. 5, 1385--1409 (2018; Zbl 1404.35121) Full Text: DOI arXiv
Nadirashvili, Nikolai S.; Penskoi, Alexei V. An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane. (English) Zbl 1400.58010 Geom. Funct. Anal. 28, No. 5, 1368-1393 (2018). MSC: 58J50 58E11 53C42 58C40 PDFBibTeX XMLCite \textit{N. S. Nadirashvili} and \textit{A. V. Penskoi}, Geom. Funct. Anal. 28, No. 5, 1368--1393 (2018; Zbl 1400.58010) Full Text: DOI arXiv
Ho, Pak Tung A characterization of the disk by eigenfunction of the Steklov eigenvalue. (English) Zbl 1378.58027 Manuscr. Math. 154, No. 3-4, 297-307 (2017). MSC: 58J50 53A30 58C40 PDFBibTeX XMLCite \textit{P. T. Ho}, Manuscr. Math. 154, No. 3--4, 297--307 (2017; Zbl 1378.58027) Full Text: DOI
Cockburn, Bernardo; Fu, Guosheng A systematic construction of finite element commuting exact sequences. (English) Zbl 1369.65145 SIAM J. Numer. Anal. 55, No. 4, 1650-1688 (2017). MSC: 65N30 58A12 PDFBibTeX XMLCite \textit{B. Cockburn} and \textit{G. Fu}, SIAM J. Numer. Anal. 55, No. 4, 1650--1688 (2017; Zbl 1369.65145) Full Text: DOI arXiv
Imbert-Gérard, Lise-Marie; Greengard, Leslie Pseudo-spectral methods for the Laplace-Beltrami equation and the Hodge decomposition on surfaces of genus one. (English) Zbl 1397.65303 Numer. Methods Partial Differ. Equations 33, No. 3, 941-955 (2017). MSC: 65N35 35R01 58A14 PDFBibTeX XMLCite \textit{L.-M. Imbert-Gérard} and \textit{L. Greengard}, Numer. Methods Partial Differ. Equations 33, No. 3, 941--955 (2017; Zbl 1397.65303) Full Text: DOI arXiv
Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces. (English) Zbl 1362.35199 ESAIM, Control Optim. Calc. Var. 23, No. 2, 685-720 (2017). MSC: 35P15 49Q10 65N25 58J50 58C40 35A15 35R01 PDFBibTeX XMLCite \textit{C.-Y. Kao} et al., ESAIM, Control Optim. Calc. Var. 23, No. 2, 685--720 (2017; Zbl 1362.35199) Full Text: DOI arXiv
Jammes, Pierre Spectrum and conformal geometry of compact manifolds with boundary. (Spectre et géométrie conforme des variétés compactes à bord.) (French. English summary) Zbl 1321.58025 Compos. Math. 150, No. 12, 2112-2126 (2014). Reviewer: Claude Zuily (Orsay) MSC: 58J50 35P15 58C40 PDFBibTeX XMLCite \textit{P. Jammes}, Compos. Math. 150, No. 12, 2112--2126 (2014; Zbl 1321.58025) Full Text: DOI arXiv
Petrides, Romain Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces. (English) Zbl 1310.58022 Geom. Funct. Anal. 24, No. 4, 1336-1376 (2014). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 53C21 30F10 PDFBibTeX XMLCite \textit{R. Petrides}, Geom. Funct. Anal. 24, No. 4, 1336--1376 (2014; Zbl 1310.58022) Full Text: DOI arXiv
Canzani, Yaiza; Jakobson, Dmitry; Wigman, Igor Scalar curvature and \(Q\)-curvature of random metrics. (English) Zbl 1314.53070 J. Geom. Anal. 24, No. 4, 1982-2019 (2014). Reviewer: Renato G. Bettiol (Philadelphia) MSC: 53C21 53A30 58J50 58D17 58D20 60G60 PDFBibTeX XMLCite \textit{Y. Canzani} et al., J. Geom. Anal. 24, No. 4, 1982--2019 (2014; Zbl 1314.53070) Full Text: DOI
Colbois, Bruno; El Soufi, Ahmad Extremal eigenvalues of the Laplacian on Euclidean domains and closed surfaces. (English) Zbl 1301.35063 Math. Z. 278, No. 1-2, 529-546 (2014). MSC: 35P15 35R01 58J50 58E11 PDFBibTeX XMLCite \textit{B. Colbois} and \textit{A. El Soufi}, Math. Z. 278, No. 1--2, 529--546 (2014; Zbl 1301.35063) Full Text: DOI arXiv
Kropinski, Mary Catherine A.; Nigam, Nilima Fast integral equation methods for the Laplace-Beltrami equation on the sphere. (English) Zbl 1302.65262 Adv. Comput. Math. 40, No. 2, 577-596 (2014). MSC: 65N38 35J25 58J05 PDFBibTeX XMLCite \textit{M. C. A. Kropinski} and \textit{N. Nigam}, Adv. Comput. Math. 40, No. 2, 577--596 (2014; Zbl 1302.65262) Full Text: DOI arXiv
Kokarev, Gerasim Variational aspects of Laplace eigenvalues on Riemannian surfaces. (English) Zbl 1296.58020 Adv. Math. 258, 191-239 (2014). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 58E11 30F10 49R05 PDFBibTeX XMLCite \textit{G. Kokarev}, Adv. Math. 258, 191--239 (2014; Zbl 1296.58020) Full Text: DOI arXiv
Schoen, Richard Existence and geometric structure of metrics on surfaces which extremize eigenvalues. (English) Zbl 1336.53070 Bull. Braz. Math. Soc. (N.S.) 44, No. 4, 777-807 (2013). Reviewer: Magdalena Daniela Toda (Lubbock) MSC: 53C42 53A10 58J50 53C43 53-02 PDFBibTeX XMLCite \textit{R. Schoen}, Bull. Braz. Math. Soc. (N.S.) 44, No. 4, 777--807 (2013; Zbl 1336.53070) Full Text: DOI
Penskoi, Alexei V. Extremal spectral properties of Otsuki tori. (English) Zbl 1271.58007 Math. Nachr. 286, No. 4, 379-391 (2013). Reviewer: Nicolai K. Smolentsev (Kemerovo) MSC: 58E11 58J50 49R05 58D17 PDFBibTeX XMLCite \textit{A. V. Penskoi}, Math. Nachr. 286, No. 4, 379--391 (2013; Zbl 1271.58007) Full Text: DOI arXiv
Strohmaier, Alexander; Uski, Ville An algorithm for the computation of eigenvalues, spectral zeta functions and zeta-determinants on hyperbolic surfaces. (English) Zbl 1261.65113 Commun. Math. Phys. 317, No. 3, 827-869 (2013); correction ibid. 359, No. 1, 427-427 (2018). Reviewer: Marius Ghergu (Dublin) MSC: 65N25 35J05 35P15 58J05 65N12 11M41 PDFBibTeX XMLCite \textit{A. Strohmaier} and \textit{V. Uski}, Commun. Math. Phys. 317, No. 3, 827--869 (2013; Zbl 1261.65113) Full Text: DOI arXiv Backlinks: MO
Klein, C.; Kokotov, A.; Korotkin, D. Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces. (English) Zbl 1210.58025 Math. Z. 261, No. 1, 73-108 (2009). MSC: 58J52 14H15 32G15 PDFBibTeX XMLCite \textit{C. Klein} et al., Math. Z. 261, No. 1, 73--108 (2009; Zbl 1210.58025) Full Text: DOI arXiv
Lapointe, Hugues Spectral properties of bipolar minimal surfaces in \(\mathbb S^4\). (English) Zbl 1139.58025 Differ. Geom. Appl. 26, No. 1, 9-22 (2008). Reviewer: Salah Mehdi (Nanterre) MSC: 58J50 53A10 PDFBibTeX XMLCite \textit{H. Lapointe}, Differ. Geom. Appl. 26, No. 1, 9--22 (2008; Zbl 1139.58025) Full Text: DOI arXiv
Colbois, Bruno; Dryden, Emily B.; El Soufi, Ahmad Extremal \(G\)-invariant eigenvalues of the Laplacian of \(G\)-invariant metrics. (English) Zbl 1127.58026 Math. Z. 258, No. 1, 29-41 (2008). MSC: 58J50 58E11 35P15 PDFBibTeX XMLCite \textit{B. Colbois} et al., Math. Z. 258, No. 1, 29--41 (2008; Zbl 1127.58026) Full Text: DOI arXiv
Jakobson, Dmitry; Levitin, Michael; Nadirashvili, Nikolai; Polterovich, Iosif Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond. (English) Zbl 1121.58027 J. Comput. Appl. Math. 194, No. 1, 141-155 (2006). Reviewer: Zhiqin Lu (Irvine) MSC: 58J53 58J50 35P15 58J32 PDFBibTeX XMLCite \textit{D. Jakobson} et al., J. Comput. Appl. Math. 194, No. 1, 141--155 (2006; Zbl 1121.58027) Full Text: DOI arXiv
Lewis, Debra; Nigam, Nilima; Olver, Peter J. Connections for general group actions. (English) Zbl 1086.58006 Commun. Contemp. Math. 7, No. 3, 341-374 (2005). Reviewer: Neculai Papaghiuc (Iaşi) MSC: 58D19 53C15 PDFBibTeX XMLCite \textit{D. Lewis} et al., Commun. Contemp. Math. 7, No. 3, 341--374 (2005; Zbl 1086.58006) Full Text: DOI arXiv