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Mosc. Math. J., 2012, Volume 12, Number 1, Pages 173–192 (Mi mmj452)  

This article is cited in 9 scientific papers (total in 9 papers)

Extremal spectral properties of Lawson tau-surfaces and the Lamé equation

Alexei V. Penskoiabc

a Department of Geometry and Topology, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia
b Independent University of Moscow, Moscow, Russia
c Department of Mathematical Modelling (FN-12), Faculty of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia

Abstract: Extremal spectral properties of Lawson tau-surfaces are investigated. The Lawson tau-surfaces form a two-parametric family of tori or Klein bottles minimally immersed in the standard unitary three-dimensional sphere. A Lawson tau-surface carries an extremal metric for some eigenvalue of the Laplace–Beltrami operator. Using theory of the Lamé equation we find explicitly these extremal eigenvalues.

Key words and phrases: Lawson minimal surfaces, extremal metric, Lamé equation, Magnus–Winkler–Ince equation.

DOI: https://doi.org/10.17323/1609-4514-2012-12-1-173-192

Full text: http://www.ams.org/.../abst12-1-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 58E11, 58J50
Received: January 10, 2011; in revised form October 18, 2011
Language:

Citation: Alexei V. Penskoi, “Extremal spectral properties of Lawson tau-surfaces and the Lamé equation”, Mosc. Math. J., 12:1 (2012), 173–192

Citation in format AMSBIB
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\by Alexei~V.~Penskoi
\paper Extremal spectral properties of Lawson tau-surfaces and the Lam\'e equation
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 173--192
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\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-173-192}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952430}
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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. Penskoi A.V., “Extremal Spectral Properties of Otsuki Tori”, Math. Nachr., 286:4 (2013), 379–391  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. A. Karpukhin, “Nonmaximality of known extremal metrics on torus and Klein bottle”, Sb. Math., 204:12 (2013), 1728–1744  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. V. Penskoi, “Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces”, Russian Math. Surveys, 68:6 (2013), 1073–1130  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Karpukhin M.A., “Spectral Properties of Bipolar Surfaces to Otsuki Tori”, J. Spectr. Theory, 4:1 (2014), 87–111  crossref  mathscinet  zmath  isi  elib  scopus
    5. Penskoi A.V., “Generalized Lawson Tori and Klein Bottles”, J. Geom. Anal., 25:4 (2015), 2645–2666  crossref  mathscinet  zmath  isi  elib  scopus
    6. Karpukhin M., “Spectral Properties of a Family of Minimal Tori of Revolution in the Five-Dimensional Sphere”, Can. Math. Bul.-Bul. Can. Math., 58:2 (2015), 285–296  crossref  mathscinet  zmath  isi  scopus
    7. Broderick Causley, “Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces”, SIGMA, 12 (2016), 009, 11 pp.  mathnet  crossref
    8. M. A. Karpukhin, “Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces”, Int. Math. Res. Notices, 2016, no. 20, 6200–6209  crossref  mathscinet  isi  scopus
    9. Nadirashvili N.S. Penskoi V A., “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
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