Deformations of unbounded convex bodies and hypersurfaces

Details Deformations of unbounded convex bodies and hypersurfaces Deformations of unbounded convex bodies and hypersurfaces

2009-12-15

arxiv.org/abs/0912.2780v2

Mathematics

Differential Geometry

24 pages, 5 figures

Scientific paper

We study the topology of the space $\d\K^n$ of complete convex hypersurfaces of $\R^n$ which are homeomorphic to $\R^{n-1}$. In particular, using Minkowski sums, we construct a deformation retraction of $\d\K^n$ onto the Grassmannian space of hyperplanes. So every hypersurface in $\d \K^n$ 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 $\d\K^n$ consisting of smooth, strictly convex, or positively curved hypersurfaces are each contractible, which settles a question of H. Rosenberg.

Affiliated with

Also associated with

No associations

Rating

Deformations of unbounded convex bodies and hypersurfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformations of unbounded convex bodies and hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformations of unbounded convex bodies and hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-304708