The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces
Adamowicz, T., Jääskeläinen, J., & Koski, A. (2020). The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces. Revista Matematica Iberoamericana, 36(6), 1779-1834. https://doi.org/10.4171/rmi/1183
Published inRevista Matematica Iberoamericana
DisciplineMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis 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)Academy of Finland; European Commission
Funding program(s)Postdoctoral Researcher, AoF; FP7 (EU's 7th Framework Programme)
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.
Additional information about fundingT. Adamowicz was supported by a grant of National Science Center, Poland (NCN), UMO2013/09/D/ST1/03681. J. Jääskeläinen was supported by the Academy of Finland (318636 and 276233). A. Koski was supported by the Väisälä Foundation and the ERC Starting Grant number 307023.
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