New degeneration phenomenon for infinite-type Riemann surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910645785460736 |
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| author | Matsuda, Ryo |
| author_facet | Matsuda, Ryo |
| contents | Since the Teichmüller space of a surface $R$ is a deformation space of complex structures defined on $R$, its Bers boundary describes the degeneration of complex structures in a certain sense. In this paper, constructing a concrete example, we prove that if S is a Riemann surface of infinite type, there exists a Riemann surface with the marking, which is homeomorphic to the surface $R$ in the Bers boundary. We also show that many such degenerations exist in the Bers boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New degeneration phenomenon for infinite-type Riemann surfaces Matsuda, Ryo Geometric Topology Complex Variables Since the Teichmüller space of a surface $R$ is a deformation space of complex structures defined on $R$, its Bers boundary describes the degeneration of complex structures in a certain sense. In this paper, constructing a concrete example, we prove that if S is a Riemann surface of infinite type, there exists a Riemann surface with the marking, which is homeomorphic to the surface $R$ in the Bers boundary. We also show that many such degenerations exist in the Bers boundary. |
| title | New degeneration phenomenon for infinite-type Riemann surfaces |
| topic | Geometric Topology Complex Variables |
| url | https://arxiv.org/abs/2405.04178 |