Affine complete locally convex hypersurfaces |
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| Authors: | Neil S Trudinger Xu-Jia Wang |
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| Institution: | (1) Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia (e-mail: Neil.Trudinger@maths.anu.edu.au, Wang@maths.anu.edu.au), AU |
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| 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≥2. In this paper we give the affirmative answer. As an application, it follows that an affine complete, affine maximal surface
in R
3 must be an elliptic paraboloid.
Oblatum 16-VI-2001 & 27-II-2002?Published online: 29 April 2002 |
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