Isospectrality for infinite-type hyperbolic surfaces with discrete length spectrum
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911462895648768 |
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| author | Fanoni, Federica Fisac, David |
| author_facet | Fanoni, Federica Fisac, David |
| contents | We prove that every family of isospectral surfaces with discrete length spectrum arising from Sunada's method is finite. Furthermore, by introducing the topological notion of surfaces with self-duplicating ends, we show that every finite group can be realized as the full isometry group of a hyperbolic structure with discrete spectrum on such a surface, if the genus is infinite. Under the same topological assumptions, we also demonstrate that the above-mentioned isospectral families can have unbounded cardinality within a fixed moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isospectrality for infinite-type hyperbolic surfaces with discrete length spectrum Fanoni, Federica Fisac, David Geometric Topology Differential Geometry We prove that every family of isospectral surfaces with discrete length spectrum arising from Sunada's method is finite. Furthermore, by introducing the topological notion of surfaces with self-duplicating ends, we show that every finite group can be realized as the full isometry group of a hyperbolic structure with discrete spectrum on such a surface, if the genus is infinite. Under the same topological assumptions, we also demonstrate that the above-mentioned isospectral families can have unbounded cardinality within a fixed moduli space. |
| title | Isospectrality for infinite-type hyperbolic surfaces with discrete length spectrum |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2602.19670 |