MATH Seminar

Title: Deformations of unbounded convex bodies and hypersurfaces
Seminar: Analysis and Differential Geometry
Speaker: Professor Mohammad Ghomi of Georgia Institute of Technology
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2010-02-23 at 4:00PM
Venue: MSC W301
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Abstract: We study the topology of the space K of complete convex hypersurfaces of n-dimensional Euclidean space which are homeomorphic to a hyperplane. In particular, using Minkowski sums, we construct a deformation retraction of K onto the Grassmannian space of hyperplanes. So every hypersurface in K may be flattened in a canonical way. Further, the total curvature of each hypersurface evolves continuously and monotonically under this deformation. We also show that, modulo proper rotations, the subspaces of K consisting of smooth, strictly convex, or positively curved hypersurfaces are each contractible, which settles a question of H. Rosenberg.