Alexei V. Penskoi, “Extremal spectral properties of Lawson tau-surfaces and the Lamé equation”, Mosc. Math. J., 2012, Volume 12, Number 1,Pages <nobr>173

This article is cited in 14 papers

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

Alexei V. Penskoi^abc

^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.

MSC: 58E11, 58J50

Received: January 10, 2011; in revised form October 18, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-1-173-192