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manuscripta mathematica

, Volume 39, Issue 2–3, pp 313–338 | Cite as

Über die endliche Lösbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten

  • Norbert Quien
Article

Abstract

We prove finiteness results of Plateau's problem for boundary curves Г in a normal chart of radius R < π/2√κ in an analytic Riemannian manifold. It is shown that for analytic Г there exist only finitely many minimal surfaces of the type of the disc bounded by Г, which represent an absolute minimum of area, and if boundary branch points are excluded, there exist only finitely many relative minima in the normal chart. If Г lies on the boundary of a strict convex manifold, there cannot exist any boundary branch points.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Norbert Quien
    • 1
  1. 1.Fb 9 MathematikUniversität des SaarlandesSaarbrücken

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