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

Shin Nayatani; Toshihiro Shoda

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arXiv · 1704.06384

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

Shin Nayatani·Toshihiro Shoda

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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.

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Shin Nayatani, Toshihiro Shoda. 2017-04-21. Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian. https://arxiv.org/abs/1704.06384

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