6533b82cfe1ef96bd1290125
RESEARCH PRODUCT
The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces
Tomasz AdamowiczAleksis KoskiJarmo Jääskeläinensubject
subharmonicityPure mathematicsFUNCTIONALSMINIMIZERSGeneral Mathematicsp-harmonic mappings01 natural sciencesJacobin matriisitMathematics - Analysis of PDEsMaximum principleBOUNDARY-REGULARITYSYSTEMSMAPSRiemannian surface111 MathematicsFOS: MathematicsComplex Variables (math.CV)0101 mathematicsMathematicsCurvatureMathematics - Complex VariablesHomotopy010102 general mathematicsConvex curveHarmonic mapUnit diskHomeomorphismInjective functionEXISTENCEUNIQUENESSmaximum principlecurvature35J47 (Primary) 58E20 35J70 35J92 (Secondary)ELLIPTIC PROBLEMSDiffeomorphismJacobianunivalentAnalysis of PDEs (math.AP)description
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 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.
year | journal | country | edition | language |
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2020-01-01 | Revista Matemática Iberoamericana |