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Degenerating
hyperbolic surfaces and spectral gaps for large genus
Yunhui Wu, Haohao Zhang and Xuwen Zhu |
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Vol. 17 (2024), No. 4, 1377–1395
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Abstract |
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We study the differences of two consecutive eigenvalues , up to , for the Laplacian on hyperbolic surfaces of genus , and show that the supremum of such spectral gaps over the moduli space has infimum limit at least as the genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established. |
Keywords
spectral gaps, min-max principle, large genus
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Mathematical Subject Classification
Primary: 32G15
Secondary: 58C40
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Milestones
Received: 25 January 2022
Revised: 29 July 2022
Accepted: 23 September 2022
Published: 17 May 2024
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Authors |
| Yunhui Wu | |
| Yau Mathematical Sciences
Center Tsinghua University Beijing China |
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| Haohao Zhang | |
| Tsinghua University Beijing China |
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| Xuwen Zhu | |
| Department of Mathematics Northeastern University Boston, MA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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