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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 767–775 (Mi mmj586)  

This article is cited in 4 scientific papers (total in 4 papers)

Maximization of higher order eigenvalues and applications

Nikolai Nadirashvilia, Yannick Sireb

a CNRS, I2M UMR 7353 — Centre de Mathématiques et Informatique, Marseille, France
b Université Aix-Marseille, I2M UMR 7353 — Centre de Math matiques et Informatique, Marseille, France

Abstract: The present paper is a follow up of our paper “Conformal spectrum and harmonic maps”. We investigate here the maximization of higher order eigenvalues in a conformal class on a smooth compact boundaryless Riemannian surface. Contrary to the case of the first nontrivial eigenvalue as shown in the above-mentioned paper, bubbling phenomena appear.

Key words and phrases: eigenvalues, isoperimetric inequalities.

DOI: https://doi.org/10.17323/1609-4514-2015-15-4-767-775

Full text: http://www.mathjournals.org/.../2015-015-004-012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 35P15
Received: April 9, 2015
Language:

Citation: Nikolai Nadirashvili, Yannick Sire, “Maximization of higher order eigenvalues and applications”, Mosc. Math. J., 15:4 (2015), 767–775

Citation in format AMSBIB
\Bibitem{NadSir15}
\by Nikolai~Nadirashvili, Yannick~Sire
\paper Maximization of higher order eigenvalues and~applications
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 767--775
\mathnet{http://mi.mathnet.ru/mmj586}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-767-775}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438833}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900012}


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    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:
    1. N. Nadirashvili, Ya. Sire, “Isoperimetric inequality for the third eigenvalue of the Laplace–Beltrami operator on $\mathbb{S}^2$”, J. Differ. Geom., 107:3 (2017), 561–571  crossref  mathscinet  zmath  isi
    2. N. S. Nadirashvili, V A. 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  crossref  mathscinet  zmath  isi  scopus
    3. R. Petrides, “On the existence of metrics which maximize Laplace eigenvalues on surfaces”, Int. Math. Res. Notices, 2018, no. 14, 4261–4355  crossref  mathscinet  zmath  isi  scopus
    4. S. Ariturk, “An annulus and a half-helicoid maximize Laplace eigenvalues”, J. Spectr. Theory, 8:2 (2018), 315–346  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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