Minkowski type theorems for convex sets in cones
Metric Geometry
2020-08-18 v1
Abstract
Minkowski's classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface area measure of a convex body. The solution is unique up to a translation. We deal with corresponding questions for unbounded convex sets, whose behavior at infinity is determined by a given closed convex cone. We provide an existence theorem and a stability result.
Cite
@article{arxiv.2008.07248,
title = {Minkowski type theorems for convex sets in cones},
author = {Rolf Schneider},
journal= {arXiv preprint arXiv:2008.07248},
year = {2020}
}