manuscripta mathematica

, Volume 40, Issue 1, pp 27–77

Geometrische Methoden zur Gewinnung von A-Priori-Schranken für harmonische Abbildungen

  • Jürgen Jost
  • Hermann Karcher

DOI: 10.1007/BF01168235

Cite this article as:
Jost, J. & Karcher, H. Manuscripta Math (1982) 40: 27. doi:10.1007/BF01168235


In this paper, we prove a-priori estimates for harmonic mappings between Riemannian manifolds which solve a Dirichlet problem. These estimates employ geometrical methods and depend only on geometric quantities, namely curvature bounds, injectivity radii, and dimensions. An essential tool is the introduction of almost linear functions on Riemannian manifolds. Furthermore, we show the existence of almost linear and harmonic coordinates on fixed (curvature controlled) balls. These coordinates possess better regularity properties than Riemannian normal coordinates.

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Jürgen Jost
    • 1
  • Hermann Karcher
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonn 1

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