The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves

Abstract

We consider the correspondence between the space of $p$-Weil-Petersson curves $\gamma$ on the plane and the $p$-Besov space of $u=\log {\gamma }^{\prime }$ on the real line for $p>1$. We prove that the variant of the Beurling-Ahlfors extension defined by using the heat kernel yields a holomorphic map for $u$ on a domain of the $p$-Besov space to the space of $p$-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of $p$-integrable Beltrami coefficients to the $p$-Weil-Petersson Teichmüller space.

To appear in Journal of Geometric Analysis

Cited by in corpus (1)

• The $p$-integrable Teichmüller space for $p⩾1$