A result on large surfaces of prescribed mean curvature in a Riemannian manifold |
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Authors: | Norbert Jakobowsky |
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Institution: | (1) Institut für Mathematik der RWTH, Templergraben 55, D-52062 Aachen, DE |
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Abstract: | Plateau's problem (PP) is studied for surfaces of prescribed mean curvature spanned by a given contour in a 3-d Riemannian
manifold. We consider the local situation where a neighborhood of a given point on the manifold is described by a single normal
chart. Under certain conditions on and the contour, existence of a small -surface to (PP) is guaranteed by HK]. The purpose of this paper is the investigation of large -surfaces. Our result states: For sufficiently large (constant) mean curvature and a sufficiently small contour depending
on the local geometry of the manifold, (PP) has at least two solutions, a small one and a large one. The proof is based on
mountain pass arguments and uses – in contrast to results in the 3-d Euclidean space and in order to derive conformality directly
– also a deformation constructed by variations of the independent variable.
Received November 8, 1995 / Accepted April 29, 1996 |
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Keywords: | Mathematics Subject Classifications (1991):53A10 53A35 |
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