Abstract

We interpolate a new family of Teichmüller spaces $T_{♯}^X$ between the universal Teichmüller space $T$ and its little subspace $T_0$. Each $T_{♯}^X$ is defined by prescribing a subset $X$ of the unit circle as the exceptional set of the vanishing property for $T_0$. The inclusion relation of $X$ induces a natural inclusion of $T_{♯}^X$, and an approximation of $T$ by an increasing sequence of $T_{♯}^X$ is investigated. In this paper, we discuss the fundamental properties of $T_{♯}^X$ from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of $T$ by $T_{♯}^X$ as an analog of the asymptotic Teichmüller space.

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Mathematical Subject Classification 2010

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