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Research Report MRR01-017
On locally convex hypersurfaces with boundary
Neil S. Trudinger and Xu-Jia Wang
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.
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