On the volume of sums of anti-blocking bodies
Metric Geometry
2024-09-24 v1 Functional Analysis
Abstract
We study inequalities on the volume of Minkowski sum in the class of anti-blocking bodies. We prove analogues of Pl\"unnecke-Ruzsa type inequality and V. Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We also study Firey sums of anti-blocking bodies and prove Pl\"unnecke-Ruzsa type inequality; V. Milman inequality and Roger-Shephard inequality. The sharp constants are provided in all of those inequalities, for the class of anti-blocking bodies. Finally, we extend our results to the case of unconditional product measures with decreasing density.
Keywords
Cite
@article{arxiv.2409.14214,
title = {On the volume of sums of anti-blocking bodies},
author = {Auttawich Manui and Cheikh Saliou Ndiaye and Artem Zvavitch},
journal= {arXiv preprint arXiv:2409.14214},
year = {2024}
}