A1 Journal article (refereed)
The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces (2020)


Adamowicz, Tomasz; Jääskeläinen, Jarmo; Koski, Aleksis (2020). The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces. Revista Matematica Iberoamericana, 36 (6), 1779-1834. DOI: 10.4171/rmi/1183


JYU authors or editors


Publication details

All authors or editors: Adamowicz, Tomasz; Jääskeläinen, Jarmo; Koski, Aleksis

Journal or series: Revista Matematica Iberoamericana

ISSN: 0213-2230

eISSN: 2235-0616

Publication year: 2020

Volume: 36

Issue number: 6

Pages range: 1779-1834

Publisher: European Mathematical Society Publishing House

Publication country: Switzerland

Publication language: English

DOI: http://doi.org/10.4171/rmi/1183

Open Access: Publication channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68367

Publication is parallel published: https://arxiv.org/abs/1806.03020


Abstract

In the planar setting, the Radó–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 Radó–Kneser–Choquet for p-harmonic mappings between Riemannian surfaces.

In our proof of the injectivity criterion we approximate the p-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expression that is related to the Jacobian.


Keywords: Jacobians

Free keywords: curvature; Jacobian; maximum principle; p-harmonic mappings; Riemannian surface; subharmonicity; univalent


Contributing organizations


Related projects

Nonlinear Elliptic Equations, Quasiharmonic Fields, and the Range of the Differential
Jääskeläinen, Jarmo
Academy of Finland
01/09/2017-28/02/2018


Ministry reporting: Yes

Preliminary JUFO rating: 2


Last updated on 2020-28-10 at 08:53