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

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

2010-09-01

arxiv.org/abs/1009.0285v5

Moscow Mathematical Journal 12 (2012), no. 1, 173-192

Mathematics

Spectral Theory

LaTeX, 17 pages; v5: typos corrected. arXiv admin note: supercedes arXiv:1008.2954

Scientific paper

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 Lam\'e equation we find explicitly these extremal eigenvalues.

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