Radó–Kneser–Choquet theorem for harmonic mappings between surfaces

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• 作者：David Kalaj
• 关键词：Mathematics Subject ClassificationPrimary 47B35
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：56
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0835
• 卷排序：56

文摘

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.