Work

On the volume of sums of anti-blocking convex bodies

Year: 2025

Type: article

Abstract: In this paper, we study volume inequalities of Minkowski sum in the class of anti-blocking convex bodies. We prove analogues of a Plünnecke–Ruzsa-type inequality and Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We also study Firey [Formula: see text]-sums of anti-blocking convex bodies, and prove a Plünnecke–Ruzsa-type inequality, Milman inequality and Rogers–Shephard inequality. The sharp constants are provided in all of those inequalities, for the class of anti-blocking convex bodies. Finally, we extend our results to the case of unconditional product measures with non-increasing density.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500956

Authors: Auttawich Manui, Cheikh Saliou Ndiaye, Artem Zvavitch

Institutions: Kent State University, Centre National de la Recherche Scientifique, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Harmonic Analysis in Convex Geometry, Harmonic Analysis in Convex Geometry