The 𝐿_{𝑝} Brunn-Minkowski inequalities for dual quermassintegrals

Xi, Dongmeng; Zhang, Zhenkun

doi:10.1090/proc/15952

The $L_p$ Brunn-Minkowski inequalities for dual quermassintegrals
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by Dongmeng Xi and Zhenkun Zhang PDF

Proc. Amer. Math. Soc. 150 (2022), 3075-3086 Request permission

Abstract:

From a convex geometry viewpoint, we proved the $L_p$ Brunn-Minkowski inequalities for $q$-th dual quermassintegrals, when $p\geq q$.

Based on these inequalities, we obtain relevant uniqueness results of the $(p,q)$-th dual curvature measures (up to a dilation when $p=q$). As a special case $q=0$, we obtain the uniqueness of $L_p$ integral curvature measure. Part of these uniqueness results were obtained before from different viewpoints.

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