Extremal spectral properties of Otsuki tori
Spectral Theory
2013-02-22 v3 Differential Geometry
Abstract
Otsuki tori form a countable family of immersed minimal two-dimensional tori in the unitary three-dimensional sphere. According to El Soufi-Ilias theorem, the metrics on the Otsuki tori are extremal for some unknown eigenvalues of the Laplace-Beltrami operator. Despite the fact that the Otsuki tori are defined in quite an implicit way, we find explicitly the numbers of the corresponding extremal eigenvalues. In particular we provide an extremal metric for the third eigenvalue of the torus.
Keywords
Cite
@article{arxiv.1108.5160,
title = {Extremal spectral properties of Otsuki tori},
author = {Alexei V. Penskoi},
journal= {arXiv preprint arXiv:1108.5160},
year = {2013}
}
Comments
14 pages, 1 figure. v.2: minor corrections v.3: references are updated. arXiv admin note: text overlap with arXiv:1009.0285