Spectral Gaps on Large Hyperbolic Surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914266295042048 |
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| author | Monk, Laura Naud, Frédéric |
| author_facet | Monk, Laura Naud, Frédéric |
| contents | In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the investigation of the first non-trivial eigenvalue $λ_1$ and its possible behaviour in the large volume regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Gaps on Large Hyperbolic Surfaces Monk, Laura Naud, Frédéric Spectral Theory Primary 58J50, 32G15, 20C30. Secondary 05C80, 20P05, 11F72 In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the investigation of the first non-trivial eigenvalue $λ_1$ and its possible behaviour in the large volume regime. |
| title | Spectral Gaps on Large Hyperbolic Surfaces |
| topic | Spectral Theory Primary 58J50, 32G15, 20C30. Secondary 05C80, 20P05, 11F72 |
| url | https://arxiv.org/abs/2601.13988 |