# MathSciDoc: An Archive for Mathematician ∫

#### Complex Variables and Complex Analysismathscidoc:1611.08002

Monatsh Math. , 181, (1), 235-244, 2016.6
Let $T(S)$ be the Teichmuller space over a hyperbolic Riemann surface $S$. A geodesic disk in $T(S)$ is defined the image of an isometric embedding of the Poincar\'e disk into $T(S)$. In this paper, it is shown that for any non-Strebel point $\tau\in T(S)\backslash\{[0]\}$, there are infinitely many geodesic disks containing the straight line $\{[t\mu]:\,t\in (-1/k,1/k)\}$ where $\mu$ is an extremal representative of $\tau$ with $\|\mu\|_\infty=k$. An infinitesimal version is also obtained.
Teichmuller space, non-Strebel point, geodesic disk, geodesic plane
@inproceedings{guowu2016on,
title={On nonuniqueness of geodesic disks in infinite-dimensional Teichmüller spaces},
author={Guowu Yao},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161123162244705767629},
booktitle={ Monatsh Math.  },
volume={181},
number={1},
pages={235-244},
year={2016},
}

Guowu Yao. On nonuniqueness of geodesic disks in infinite-dimensional Teichmüller spaces. 2016. Vol. 181. In Monatsh Math. . pp.235-244. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161123162244705767629.