English

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 W1,2W^{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.

Keywords

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

R2 v1 2026-06-21T15:41:29.335Z