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arXiv · 2201.03056

Degenerating hyperbolic surfaces and spectral gaps for large genus

Yunhui Wu·Haohao Zhang·Xuwen Zhu
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Abstract

In this article we study the differences of two consecutive eigenvalues $λ_{i}-λ_{i-1}$ up to $i=2g-2$ for the Laplacian on hyperbolic surfaces of genus $g$, and show that the supremum of such spectral gaps over the moduli space has infimum limit at least $\frac{1}{4}$ as genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established.

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Yunhui Wu, Haohao Zhang, Xuwen Zhu. 2022-09-26. Degenerating hyperbolic surfaces and spectral gaps for large genus. https://doi.org/10.2140/apde.2024.17.1377

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