The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces
Finna-arvio
The Radó-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces
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.
Tallennettuna:
Kieli |
englanti |
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Sarja | Revista Matematica Iberoamericana, 6 |
Aiheet | |
ISSN |
0213-2230 |