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• W2952223369 abstract "We consider a functional $mathcal F$ on the space of convex bodies in $R^n$ defined as follows: ${mathcal F}(K)$ is the integral over the unit sphere of a fixed continuous functions $f$ with respect to the area measure of the convex body $K$. We prove that if $mathcal F$ satisfies an inequality of Brunn--Minkowski type, then $f$ is the support function of a convex body, i.e., $mathcal F$ is a mixed volume. As a consequence, we obtain a characterization of translation invariant, continuous valuations which are homogeneous of degree $n-1$ and satisfy a Brunn--Minkowski type inequality." @default.
• W2952223369 created "2019-06-27" @default.
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• W2952223369 date "2012-02-10" @default.
• W2952223369 modified "2023-09-27" @default.
• W2952223369 title "A characterization of some mixed volumes via the Brunn-Minkowski inequality" @default.
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• W2952223369 hasPublicationYear "2012" @default.
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