Asymptotic conformality of the Barycentric extension of quasiconformal maps

Katsuhiko Matsuzaki, Masahiro Yanagishita

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface R obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of R. Then we give a new proof, without using the Bers embedding, of a fact that the quasiconformal homeomorphism obtained by the barycentric extension from an integrable Beltrami coefficient on R is asymptotically conformal if R satisfies a certain geometric condition.

Original languageEnglish
Pages (from-to)85-90
Number of pages6
JournalFilomat
Volume31
Issue number1
DOIs
Publication statusPublished - 2017

Keywords

  • Asymptotically conformal
  • Barycentric extension
  • Bers embedding
  • Complex dilatation
  • Integrable teichmüller space
  • Quasiconformal
  • Teichmüller projection

ASJC Scopus subject areas

  • Mathematics(all)

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