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arXiv · 1006.5174

Hopf differentials and smoothing Sobolev homeomorphisms

Tadeusz Iwaniec·Leonid V. Kovalev·Jani Onninen
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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.

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Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen. 2010-06-27. Hopf differentials and smoothing Sobolev homeomorphisms. https://doi.org/10.1093/imrn%2Frnr144

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