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Radó–Kneser–Choquet theorem for harmonic mappings between surfaces

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Abstract

We simplify and improve a recent result of Martin (Trans AMS 368:647–658, 2016). Then we prove that if f is an orientation preserving harmonic mapping of the unit disk onto a \(C^{3,\alpha }\) surface \(\Sigma \) bounded by a Jordan curve \(\gamma \in C^{3,\alpha }\), that belongs to the boundary of a convex domain in \(\mathbf {R}^3\), then f is a diffeomorphism.

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Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski Put B.B., 81000, Podgorica, Montenegro

    David Kalaj

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  1. David Kalaj
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Correspondence to David Kalaj.

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Communicated by J. Jost.

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Kalaj, D. Radó–Kneser–Choquet theorem for harmonic mappings between surfaces. Calc. Var. 56, 4 (2017). https://doi.org/10.1007/s00526-016-1098-0

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