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arXiv · 2107.01287

On $p$-Brunn-Minkowski inequalities for intrinsic volumes with $0\leq p<1$

C. Bianchini·A. Colesanti·D. Pagnini·A. Roncoroni
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Abstract

We prove the validity of the $p$-Brunn-Minkowski inequality for the intrinsic volume $V_k$, $k=2,\dots, n-1$, of convex bodies in $\mathbb{R}^n$, in a neighborhood of the unit ball, for $0\le p<1$. We also prove that this inequality does not hold true on the entire class of convex bodies of $\mathbb{R}^n$, when $p$ is sufficiently close to $0$.

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C. Bianchini, A. Colesanti, D. Pagnini, A. Roncoroni. 2021-07-02. On $p$-Brunn-Minkowski inequalities for intrinsic volumes with $0\leq p<1$. https://arxiv.org/abs/2107.01287

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