|
This article is cited in 10 scientific papers (total in 10 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)
References:
PDF file
HTML file
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
\Bibitem{Pen13}
\by A.~V.~Penskoi
\paper Extremal metrics for eigenvalues of the Laplace--Beltrami operator on surfaces
\jour Uspekhi Mat. Nauk
\yr 2013
\vol 68
\issue 6(414)
\pages 107--168
\mathnet{http://mi.mathnet.ru/umn9565}
\crossref{https://doi.org/10.4213/rm9565}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3203194}
\zmath{https://zbmath.org/?q=an:06286871}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013RuMaS..68.1073P}
\elib{https://elibrary.ru/item.asp?id=21277013}
\transl
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 6
\pages 1073--1130
\crossref{https://doi.org/10.1070/RM2013v068n06ABEH004870}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000332667100003}
\elib{https://elibrary.ru/item.asp?id=21917449}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899749314}
Linking options:
http://mi.mathnet.ru/eng/umn9565https://doi.org/10.4213/rm9565 http://mi.mathnet.ru/eng/umn/v68/i6/p107
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
N. Kuznetsov, A. Nazarov, “Sharp constants in the Poincaré, Steklov and related inequalities (a survey)”, Mathematika, 61:2 (2015), 328–344
-
Broderick Causley, “Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces”, SIGMA, 12 (2016), 009, 11 pp.
 -
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
-
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
-
J. Hirsch, E. Mäder-Baumdicker, “Note on Willmore minimizing Klein bottles in Euclidean space”, Adv. Math., 319 (2017), 67–75
-
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
-
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
-
Alexei V. Penskoi, “Isoperimetric Inequalities for Higher Eigenvalues of the Laplace–Beltrami Operator on Surfaces”, Proc. Steklov Inst. Math., 305 (2019), 270–286
-
Cianci D., Karpukhin M., Medvedev V., “on Branched Minimal Immersions of Surfaces By First Eigenfunctions”, Ann. Glob. Anal. Geom., 56:4 (2019), 667–690
-
Gabdurakhmanov R., “Spaces of Harmonic Maps of the Projective Plane to the Four-Dimensional Sphere”, J. Geom., 111:3 (2020), 40
|
| Number of views: |
| This page: | 643 | | Full text: | 305 | | References: | 81 | | First page: | 80 |
|
Terms of Use