The Rad\'o-Kneser-Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

T. Adamowicz; J. Jaaskelainen; Aleksis Koski

DOI:10.4171/rmi/1183

Corpus ID: 119627678

The Rad\'o-Kneser-Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

@article{Adamowicz2018TheRT,
  title={The Rad\'o-Kneser-Choquet theorem for \$p\$-harmonic mappings between Riemannian surfaces},
  author={T. Adamowicz and J. Jaaskelainen and Aleksis Koski},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}

T. Adamowicz, J. Jaaskelainen, Aleksis Koski

Published 2018

Mathematics

arXiv: Analysis of PDEs

In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each… CONTINUE READING

View PDF on arXiv