Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

Abstract

In this paper, we settle in the affirmative the Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area normalized, should maximize the first eigenvalue of the Laplacian.

21 pages, 3 figures

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