Boundary restricted Brunn-Minkowski inequalities
Metric Geometry
2024-07-30 v3
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 where and 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.
Cite
@article{arxiv.2306.15293,
title = {Boundary restricted Brunn-Minkowski inequalities},
author = {Shiri Artstein-Avidan and Tomer Falah and Boaz A. Slomka},
journal= {arXiv preprint arXiv:2306.15293},
year = {2024}
}
Comments
Previous version extended and split into three papers. This is paper no. 1; 13 pages, 3 figures, published in Communications in Contemporary Mathematics