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manuscripta mathematica

, Volume 32, Issue 1–2, pp 51–57 | Cite as

Eine geometrische Bemerkung zu Sätzen über harmonische Abbildungen, die ein Dirichletproblem lösen

  • Jürgen Jost
Article

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

  1. [1]
    CHEEGER, J., EBIN, D.: Comparison Theorems in Riemannian Geometry. North Holland Publishing Company 1975Google Scholar
  2. [2]
    GROMOLL, D., KLINGENBERG, W., MEYER, W.: Riemannsche Geometrie im Großen. Springer, Berlin-Heidelberg-New York 1968Google Scholar
  3. [3]
    HILDEBRANDT, S., KAUL, H., WIDMAN, K.-O.: An Existence Theorem for Harmonic Mappings of Riemannian Manifolds. Acta Math. 138 (1977), S. 1–16Google Scholar
  4. [4]
    JÄGER, W., KAUL, H.: Uniqueness and Stability of Harmonic Maps and their Jacobi Fields. Man. math. 28 (1979), S. 269–291Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Mathematisches Institut der Universität BonnBonn 1Bundesrepublik Deutschland

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