Abstract
Let BM(p) be a geodesic ball in a Riemannian manifold with radius\(M< \frac{\pi }{{2\sqrt K }}\), where κ is an upper bound of the sectional curvature. The cut locus condition on BM(p) occuring in several theorems on harmonic mappings which map into BM(p) can be weakened by proving uniqueness of geodesics contained in BM(p).
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Literatur
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Jost, J. Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen. Manuscripta Math 32, 51–57 (1980). https://doi.org/10.1007/BF01298181
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DOI: https://doi.org/10.1007/BF01298181