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Dual Brunn-Minkowski inequality for C-star bodies
Published 12 Dec 2023 in math.FA | (2312.07095v2)
Abstract: In this paper, we consider the concept of $C$-star body in a fixed pointed closed convex cone $C$ and study the dual mixed volume for $C$-star bodies. For $C$-star bodies, we establish the corresponding dual Brunn-Minkowski inequality, the dual Minkowski inequality and the dual Aleksandrov-Fenchel inequality. Our dual Brunn-Minkowski inequality for $C$-star bodies strengthens Schneider's Brunn-Minkowski inequality for $C$-coconvex sets.
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