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Moscow Mathematical Journal, 2012, Volume 12, Number 1, Pages 173–192
DOI: https://doi.org/10.17323/1609-4514-2012-12-1-173-192 (Mi mmj452) 		 
This article is cited in 13 scientific papers (total in 13 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
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DOI: https://doi.org/10.17323/1609-4514-2012-12-1-173-192
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.
Received: January 10, 2011; in revised form October 18, 2011
Bibliographic databases:
Document Type: Article
MSC: 58E11, 58J50
Language: English
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
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\yr 2012
\vol 12
\issue 1
\pages 173--192
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2952430}
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    • This publication is cited in the following 13 articles:
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