Maximization of the first nontrivial eigenvalue on the surface of genus two

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 $16\pi$. This provides a positive answer to the conjecture by Jakobson, Levitin, Nadirashvili, Nigam and Polterovich.

This paper has been withdrawn by the author due to a crucial mistake in the equality ${\sigma }^2=id$, which should be ${\sigma }^2=T$

Cited by in corpus (2)

• Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces
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