On the Jacobian of the Douady-Earle extension
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909966796849152 |
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| author | Connell, Chris Ruan, Yuping Wang, Shi |
| author_facet | Connell, Chris Ruan, Yuping Wang, Shi |
| contents | Given an isotopy class between two closed hyperbolic surfaces, the Douady--Earle extension provides a unique analytic diffeomorphism representative. In this paper we investigate the Jacobian of the Douady--Earle extension map $F$. We prove that $|\operatorname{Jac} F| \equiv 1$ precisely when $F$ is an isometry. Moreover, we construct a sequence of hyperbolic surfaces $\{Σ_i\}$ together with a fixed domain surface $Σ_0$ for which the Douady--Earle extension maps $F_i:Σ_0\toΣ_i$ satisfy $\max_{x\inΣ_0} \operatorname{Jac} F_i \to +\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Jacobian of the Douady-Earle extension Connell, Chris Ruan, Yuping Wang, Shi Geometric Topology Given an isotopy class between two closed hyperbolic surfaces, the Douady--Earle extension provides a unique analytic diffeomorphism representative. In this paper we investigate the Jacobian of the Douady--Earle extension map $F$. We prove that $|\operatorname{Jac} F| \equiv 1$ precisely when $F$ is an isometry. Moreover, we construct a sequence of hyperbolic surfaces $\{Σ_i\}$ together with a fixed domain surface $Σ_0$ for which the Douady--Earle extension maps $F_i:Σ_0\toΣ_i$ satisfy $\max_{x\inΣ_0} \operatorname{Jac} F_i \to +\infty$. |
| title | On the Jacobian of the Douady-Earle extension |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2512.15032 |