Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.15032 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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 $\max_{x\inΣ_0} \operatorname{Jac} F_i \to +\infty$.