The Carathéodory metric on Teichmüller space of genus two surface
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911437719339008 |
|---|---|
| author | Lin, Kejie Su, Weixu |
| author_facet | Lin, Kejie Su, Weixu |
| contents | Let $\Tei_{g,n}$ be the Teichmüller space of Riemann surfaces of genus $g$ with $n$ punctures. It is conjectured that the Teichmüller and Carathéodory metrics agree on a Teichmüller disk if and only if all the zeros of the corresponding holomorphic quadratic differential are of even order. The conjecture was proved by Gekhtman and Markovic for $\Tei_{0,5}\cong \Tei_{1,2}$. We confirm the conjecture for $\Tei_{2,0}\cong\Tei_{0,6}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Carathéodory metric on Teichmüller space of genus two surface Lin, Kejie Su, Weixu Complex Variables Geometric Topology 32G15, 30F60 Let $\Tei_{g,n}$ be the Teichmüller space of Riemann surfaces of genus $g$ with $n$ punctures. It is conjectured that the Teichmüller and Carathéodory metrics agree on a Teichmüller disk if and only if all the zeros of the corresponding holomorphic quadratic differential are of even order. The conjecture was proved by Gekhtman and Markovic for $\Tei_{0,5}\cong \Tei_{1,2}$. We confirm the conjecture for $\Tei_{2,0}\cong\Tei_{0,6}$. |
| title | The Carathéodory metric on Teichmüller space of genus two surface |
| topic | Complex Variables Geometric Topology 32G15, 30F60 |
| url | https://arxiv.org/abs/2602.09751 |