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

  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},
  • 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
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