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Asymptotically conformal classes and non-Strebel points

Guowu Yao — 2016

Studia Mathematica

Let T(Δ) be the universal Teichmüller space on the unit disk Δ and T₀(Δ) be the set of asymptotically conformal classes in T(Δ). Suppose that μ is a Beltrami differential on Δ with [μ] ∈ T₀(Δ). It is an interesting question whether [tμ] belongs to T₀(Δ) for general t ≠ 0, 1. In this paper, it is shown that there exists a Beltrami differential μ ∈ [0] such that [tμ] is a non-trivial non-Strebel point for any t ( - 1 / | | μ | | , 1 / | | μ | | ) 0 , 1 .

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