The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces
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
Published inRevista Matematica Iberoamericana
DisciplineMatematiikkaAnalysis and Dynamics Research (huippuyksikkö)MathematicsAnalysis and Dynamics Research (Centre of Excellence)
© 2020 European Mathematical Society
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.
PublisherEuropean Mathematical Society Publishing House
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Related funder(s)European Commission; Academy of Finland
Funding program(s)FP7 (EU's 7th Framework Programme); Postdoctoral Researcher, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.