Abstract
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.
Original language | English |
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Pages (from-to) | 11-32 |
Number of pages | 22 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Issue number | 551 |
DOIs | |
Publication status | Published - 2002 |