Quasi-isometric embeddings for shrinking maps from surfaces into the moduli space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915613023141888 |
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| author | Zhang, Yibo |
| author_facet | Zhang, Yibo |
| contents | We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichmüller space, we consider whether they are quasi-isometric embeddings with respect to natural metrics like the Teichmüller distance and the intrinsic distance. Under a mild condition, we prove that these properties are characterised solely by the map's monodromy. These characterisations apply, in particular, to holomorphic maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-isometric embeddings for shrinking maps from surfaces into the moduli space Zhang, Yibo Geometric Topology Metric Geometry 57 K 20, 30 F 45, 51 F 30, 37 F 34 We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichmüller space, we consider whether they are quasi-isometric embeddings with respect to natural metrics like the Teichmüller distance and the intrinsic distance. Under a mild condition, we prove that these properties are characterised solely by the map's monodromy. These characterisations apply, in particular, to holomorphic maps. |
| title | Quasi-isometric embeddings for shrinking maps from surfaces into the moduli space |
| topic | Geometric Topology Metric Geometry 57 K 20, 30 F 45, 51 F 30, 37 F 34 |
| url | https://arxiv.org/abs/2511.09317 |