Minkowski type theorems for convex sets in cones

Rolf Schneider

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arXiv · 2008.07248

Minkowski type theorems for convex sets in cones

Rolf Schneider

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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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Rolf Schneider. 2020-08-17. Minkowski type theorems for convex sets in cones. https://arxiv.org/abs/2008.07248

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