Minkowski type theorems for convex sets in cones
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,...
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Veröffentlicht in: | Acta mathematica Hungarica 2021-06, Vol.164 (1), p.282-295 |
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description | 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. |
doi_str_mv | 10.1007/s10474-020-01119-1 |
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subjects | Cones Convexity Euclidean geometry Euclidean space Existence theorems Mathematics Mathematics and Statistics |
title | Minkowski type theorems for convex sets in cones |
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