Extremal spectral properties of Lawson tori
Spectral Theory
2012-01-04 v4 Differential Geometry
Abstract
Extremal spectral properties of the Lawson tori are studied. A Lawson torus carries an extremal metric for some eigenvalue of the Laplace-Beltrami operator. The main result of this paper is that the number of this eigenvalue is expressed in terms of fundamental tones of auxiliary periodic Sturm-Liouville problems.
Keywords
Cite
@article{arxiv.1008.2954,
title = {Extremal spectral properties of Lawson tori},
author = {Alexei V. Penskoi},
journal= {arXiv preprint arXiv:1008.2954},
year = {2012}
}
Comments
This paper is withdrawn and it will not be published since the author obtained later in the paper arXiv:1009.0285 much stronger results using theory of the Lam\'e equation