The VMO-Teichmüller space and the variant of Beurling–Ahlfors extension by heat kernel

Huaying Wei, Katsuhiko Matsuzaki*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

Original languageEnglish
Pages (from-to)1739-1760
Number of pages22
JournalMathematische Zeitschrift
Volume302
Issue number3
DOIs
Publication statusPublished - 2022 Nov

Keywords

  • A-weight
  • BMO function
  • Beurling–Ahlfors extension
  • VMO Teichmüller space
  • Vanishing Carleson measure

ASJC Scopus subject areas

  • Mathematics(all)

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