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Abstract

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\} $.