On μ-conformal homeomorphisms and boundary correspondence

Vladimir Gutlyanskiǐ, Ken ichi Sakan, Toshiyuki Sugawa

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study the boundary correspondence under μ-homeomorphisms f of the open upper half-plane onto itself. Sufficient conditions are given for f to admit a homeomorphic extension to the closed half-plane with prescribed boundary regularity. The proofs are based on the modulus estimates for semiannuli in terms of directional dilatations of f which might be of independent interest.

Original languageEnglish
Pages (from-to)947-962
Number of pages16
JournalComplex Variables and Elliptic Equations
Volume58
Issue number7
DOIs
Publication statusPublished - 2013 Jul 1

Keywords

  • Beltrami equation
  • annulus
  • quasiconformal mappings
  • μ-homeomorphism

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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