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

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.Comment: 21 pages, 3 figure