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Minkowski type theorems for convex sets in cones

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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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  1. Mathematisches Institut, Albert-Ludwigs-Universität, D-79104, Freiburg i. Br., Germany

    R. Schneider

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  1. R. Schneider
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Correspondence to R. Schneider.

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Schneider, R. Minkowski type theorems for convex sets in cones. Acta Math. Hungar. 164, 282–295 (2021). https://doi.org/10.1007/s10474-020-01119-1

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  • DOI: https://doi.org/10.1007/s10474-020-01119-1

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