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This article is cited in 9 scientific papers (total in 9 papers)
Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces
A. V. Penskoiabc
a M. V. Lomonosov Moscow State
b National Research University "Higher School of Economics"
c Independent University of Moscow
Abstract:
Known results on geometric optimisation of eigenvalues of the Laplace operator are briefly reviewed, and a more detailed survey of recent results in the theory of extremal metrics on surfaces is presented.
Bibliography: 78 titles.
Keywords:
geometric optimisation of eigenvalues, extremal metrics, minimal surfaces in spheres.
DOI:
https://doi.org/10.4213/rm9565
 Full text:
PDF file (963 kB)
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English version:
Russian Mathematical Surveys, 2013, 68:6, 1073–1130
Bibliographic databases:
     
UDC:
514.76+517.9
MSC: 58J50, 53C42
Received: 24.10.2013
Citation:
A. V. Penskoi, “Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces”, Uspekhi Mat. Nauk, 68:6(414) (2013), 107–168; Russian Math. Surveys, 68:6 (2013), 1073–1130
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/umn9565https://doi.org/10.4213/rm9565 http://mi.mathnet.ru/eng/umn/v68/i6/p107
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M. A. Karpukhin, “Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces”, Int. Math. Res. Not. IMRN, 2016, no. 20, 6200–6209
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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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J. Hirsch, E. Mäder-Baumdicker, “Note on Willmore minimizing Klein bottles in Euclidean space”, Adv. Math., 319 (2017), 67–75
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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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M. S. Ermentai, “Ob odnom semeistve minimalnykh izotropnykh torov i butylok Kleina v $\mathbb{C}P^3$”, Sib. elektron. matem. izv., 16 (2019), 955–958
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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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