Über die endliche Lösbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten

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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.