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Research Report MRR01-016
Affine complete locally convex hypersurfaces
Neil S. Trudinger and Xu-Jia Wang
Abstract:
An open problem in affine geometry is whether an affine complete locally uniformly convex hypersurface
in
Euclidean (n+1)-space is Euclidean complete for n\geq 2. In this paper we give the
affirmative answer. As
an application, it follows that an affine complete, affine maximal surface in R3 must
be an elliptic
paraboloid.
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