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

Alexei V. Penskoi

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arXiv · 1009.0285

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

Alexei V. Penskoi

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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.

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Alexei V. Penskoi. 2012-01-01. Extremal spectral properties of Lawson tau-surfaces and the Lamé equation. https://arxiv.org/abs/1009.0285

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