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.

22 pages, 0 figures

Cited by in corpus (2)

• Diffeomorphic approximation of Sobolev homeomorphisms
• Lipschitz regularity for inner-variational equations