Dual Brunn-Minkowski inequality for C-star bodies

2023/12/12 by Wang, Xudong, Xiang, Tingting
#52A20 #52A39 #53C65 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2312.07095

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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