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arXiv · 1309.5057

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

Mikhail A. Karpukhin
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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 $16π$. This provides a positive answer to the conjecture by Jakobson, Levitin, Nadirashvili, Nigam and Polterovich.

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Mikhail A. Karpukhin. 2014-08-10. Maximization of the first nontrivial eigenvalue on the surface of genus two. https://arxiv.org/abs/1309.5057

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