Hopf differentials and smoothing Sobolev homeomorphisms
Complex Variables
2012-07-13 v1
Abstract
We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.
Cite
@article{arxiv.1006.5174,
title = {Hopf differentials and smoothing Sobolev homeomorphisms},
author = {Tadeusz Iwaniec and Leonid V. Kovalev and Jani Onninen},
journal= {arXiv preprint arXiv:1006.5174},
year = {2012}
}
Comments
22 pages, 0 figures