Maximization of the first nontrivial eigenvalue on the surface of genus two
Differential Geometry
2014-08-12 v2 Spectral Theory
Abstract
The first nontrivial eigenvalue of the Laplacian can be considered as a functional on the space of all Riemannian metrics of unit volume on a fixed surface. In this paper we prove that for the surface of genus 2 the supremum of this functional is equal to . This provides a positive answer to the conjecture by Jakobson, Levitin, Nadirashvili, Nigam and Polterovich.
Keywords
Cite
@article{arxiv.1309.5057,
title = {Maximization of the first nontrivial eigenvalue on the surface of genus two},
author = {Mikhail A. Karpukhin},
journal= {arXiv preprint arXiv:1309.5057},
year = {2014}
}
Comments
This paper has been withdrawn by the author due to a crucial mistake in the equality $\sigma^2 = id$, which should be $\sigma^2 = T$