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On locally convex hypersurfaces with boundary

Trudinger, Neil; Wang, Xu-Jia


In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature.

CollectionsANU Research Publications
Date published: 2002
Type: Journal article
Source: Journal fur Reine und Angewandte Mathematik


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