Hopf differentials and smoothing sobolev homeomorphisms

Tadeusz Iwaniec; Leonid V. Kovalev; Jani Onninen

doi:10.1093/imrn/rnr144

Hopf differentials and smoothing sobolev homeomorphisms

Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

39 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 language	English (US)
Pages (from-to)	3256-3277
Number of pages	22
Journal	International Mathematics Research Notices
Volume	2012
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnr144
State	Published - 2012

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnr144

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title = "Hopf differentials and smoothing sobolev homeomorphisms",

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.",

author = "Tadeusz Iwaniec and Kovalev, {Leonid V.} and Jani Onninen",

note = "Funding Information: This work was supported by the National Science Foundation (grants DMS-0800416 to T.I., DMS-0968756 to L.V.K., DMS-1001620 to J.O.); and the Academy of Finland (grant 1128331 to T.I.)",

year = "2012",

doi = "10.1093/imrn/rnr144",

language = "English (US)",

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T1 - Hopf differentials and smoothing sobolev homeomorphisms

AU - Iwaniec, Tadeusz

AU - Kovalev, Leonid V.

AU - Onninen, Jani

N1 - Funding Information: This work was supported by the National Science Foundation (grants DMS-0800416 to T.I., DMS-0968756 to L.V.K., DMS-1001620 to J.O.); and the Academy of Finland (grant 1128331 to T.I.)

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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Hopf differentials and smoothing sobolev homeomorphisms

Abstract

ASJC Scopus subject areas

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