Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings. (English) Zbl 1279.30032
Summary: 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.
MSC:
30C62 | Quasiconformal mappings in the complex plane |
30A05 | Monogenic and polygenic functions of one complex variable |
31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |