The p-Weil–Petersson Teichmüller Space and the Quasiconformal Extension of Curves

Huaying Wei*, Katsuhiko Matsuzaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the correspondence between the space of p-Weil–Petersson curves γ on the plane and the p-Besov space of u= log γ 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.

Original languageEnglish
Article number213
JournalJournal of Geometric Analysis
Volume32
Issue number8
DOIs
Publication statusPublished - 2022 Aug

Keywords

  • A-weights
  • Besov space
  • Beurling–Ahlfors extension
  • BMO functions
  • Global section of Teichmüller projection
  • Integrable Beltrami coefficients
  • Weil–Petersson Teichmüller space

ASJC Scopus subject areas

  • Geometry and Topology

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