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This article is cited in 8 scientific papers (total in 8 papers)
Nonmaximality of known extremal metrics on torus and Klein bottle
M. A. Karpukhinab
a M. V. Lomonosov Moscow State University
b Independent University of Moscow
Abstract:
The El Soufi-Ilias theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this connection was used to provide several explicit examples of extremal metrics. We investigate the properties of these metrics and prove that none of them is maximal.
Bibliography: 24 titles.
Keywords:
extremal metrics, bipolar surface, Otsuki tori, Lawson tau-surfaces.
DOI:
https://doi.org/10.4213/sm8227
 Full text:
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English version:
Sbornik: Mathematics, 2013, 204:12, 1728–1744
Bibliographic databases:
     
UDC:
514.764.21
MSC: 58E11
Received: 27.02.2013 and 10.06.2013
Citation:
M. A. Karpukhin, “Nonmaximality of known extremal metrics on torus and Klein bottle”, Mat. Sb., 204:12 (2013), 31–48; Sb. Math., 204:12 (2013), 1728–1744
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Linking options:
http://mi.mathnet.ru/eng/msb8227https://doi.org/10.4213/sm8227 http://mi.mathnet.ru/eng/msb/v204/i12/p31
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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A. V. Penskoi, “Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces”, Russian Math. Surveys, 68:6 (2013), 1073–1130
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A. V. Penskoi, “Generalized Lawson Tori and Klein Bottles”, J. Geom. Anal., 25:4 (2015), 2645–2666
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M. Karpukhin, “Spectral properties of a family of minimal tori of revolution in five-dimensional sphere”, Can. Math. Bull., 58:2 (2015), 285–296
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Broderick Causley, “Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces”, SIGMA, 12 (2016), 009, 11 pp.
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Ch.-Y. Kao, R. Lai, B. Osting, “Maximization of Laplace–Beltrami eigenvalues on closed Riemannian surfaces”, ESAIM Control Optim. Calc. Var., 23:2 (2017), 685–720
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N. S. Nadirashvili, A. V. Penskoi, “An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane”, Geom. Funct. Anal., 28:5 (2018), 1368–1393
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Alexei V. Penskoi, “Isoperimetric Inequalities for Higher Eigenvalues of the Laplace–Beltrami Operator on Surfaces”, Proc. Steklov Inst. Math., 305 (2019), 270–286
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Cianci D., Karpukhin M., Medvedev V., “On Branched Minimal Immersions of Surfaces By First Eigenfunctions”, Ann. Glob. Anal. Geom., 56:4 (2019), 667–690
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