Degenerating hyperbolic surfaces and spectral gaps for large genus
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916252744679424 |
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| author | Wu, Yunhui Zhang, Haohao Zhu, Xuwen |
| author_facet | Wu, Yunhui Zhang, Haohao Zhu, Xuwen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_03056 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Degenerating hyperbolic surfaces and spectral gaps for large genus Wu, Yunhui Zhang, Haohao Zhu, Xuwen Differential Geometry Analysis of PDEs 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. |
| title | Degenerating hyperbolic surfaces and spectral gaps for large genus |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2201.03056 |