Affine hemispheres of elliptic type
Differential Geometry
2015-12-15 v2 Metric Geometry
Abstract
We find that for any n-dimensional, compact, convex subset K of R^{n+1} there is an affinely-spherical hypersurface M in R^{n+1} with center at the relative interior of K, such that the disjoint union of M and K is the boundary of an (n+1)-dimensional, compact, convex set. This so-called affine hemisphere M is uniquely determined by K up to affine transformations, it is of elliptic type, is associated with K in an affinely-invariant manner, and it is centered at the Santalo point of K.
Cite
@article{arxiv.1508.00474,
title = {Affine hemispheres of elliptic type},
author = {Bo'az Klartag},
journal= {arXiv preprint arXiv:1508.00474},
year = {2015}
}
Comments
39 pages, minor revision