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- W4313304944 abstract "The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of these concepts to Borel measures with density in $mathbb{R}^n$-- in particular, the weighted versions of mixed volumes (the so-called mixed measures) when dealing with up to three distinct convex bodies. We then formulate and analyze weighted versions of classical surface area measures, and obtain a new integral formula for the mixed measure of three bodies. As an application, we prove a B'ezout-type inequality for rotational invariant log-concave measures, generalizing a result by Artstein-Avidan, Florentin and Ostrover. The results are new and interesting even for the special case of the standard Gaussian measure." @default.
- W4313304944 created "2023-01-06" @default.
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- W4313304944 date "2022-12-27" @default.
- W4313304944 modified "2023-09-30" @default.
- W4313304944 title "Weighted Brunn-Minkowski Theory I: On Weighted Surface Area Measures" @default.
- W4313304944 doi "https://doi.org/10.48550/arxiv.2212.13522" @default.
- W4313304944 hasPublicationYear "2022" @default.
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