Minkowski type theorems for convex sets in cones

2020/08/17 by Schneider, Rolf · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2008.07248

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.

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• The Gaussian Minkowski problem for epigraphs of convex functions

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