Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings
Volume 207 / 2011
Studia Mathematica 207 (2011), 117-136
MSC: Primary 30A05; Secondary 30C62.
DOI: 10.4064/sm207-2-2
Abstract
We extend the Rado–Choquet–Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado–Choquet–Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.
