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arXiv · 2306.15293

Boundary restricted Brunn-Minkowski inequalities

Shiri Artstein-Avidan·Tomer Falah·Boaz A. Slomka
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Abstract

In this paper we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V.~Milman regarding the volume of $\partial K+ \partial T$ where $K$ and $T$ are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of sets with connected boundary, as well as some related results.

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Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka. 2023-06-27. Boundary restricted Brunn-Minkowski inequalities. https://doi.org/10.1142/s0219199723500566

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