Hopf differentials and smoothing sobolev homeomorphisms

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36 Scopus citations

Abstract

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W 1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

Original languageEnglish (US)
Pages (from-to)3256-3277
Number of pages22
JournalInternational Mathematics Research Notices
Volume2012
Issue number14
DOIs
StatePublished - 2012

ASJC Scopus subject areas

  • Mathematics(all)

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