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Asymptotically conformal classes and non-Strebel points

Volume 233 / 2016

Guowu Yao Studia Mathematica 233 (2016), 13-24 MSC: Primary 30C75; Secondary 30C62. DOI: 10.4064/sm8329-4-2016 Published online: 5 May 2016


Let $T(\varDelta )$ be the universal Teichmüller space on the unit disk $\varDelta $ and $T_0(\varDelta )$ be the set of asymptotically conformal classes in $T(\varDelta )$. Suppose that $\mu $ is a Beltrami differential on $\varDelta $ with $[\mu ]\in T_0(\varDelta )$. It is an interesting question whether $[t\mu ]$ belongs to $T_0(\varDelta )$ for general $t\not =0, 1$. In this paper, it is shown that there exists a Beltrami differential $\mu \in [0]$ such that $[t\mu ]$ is a non-trivial non-Strebel point for any $t\in (-{1/{\| \mu \| }_\infty },{1/{\| \mu \| }_\infty })\setminus \{0,1\} $.


  • Guowu YaoDepartment of Mathematical Sciences
    Tsinghua University
    100084 Beijing, People’s Republic of China

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