2017/11/12 by François Fillastre, Fillastre, François
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG
paper · pdf · doi:10.48550/arxiv.1711.04272
2 pages with 1 figure
arxiv created 2017/11/12 · openalex publication_date 2017/11/12 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory of coconvex bodies was formalized by A.~Khovanski\uı and V.~Timorin in \citeKT. It has fascinating relations with the classical theory of convex bodies, as well as applications to Lorentzian geometry. In a recent preprint \citeschnei2, R.~Schneider proved a result that implies a reversed Brunn--Minkowski inequality for coconvex bodies, with description of equality case. In this note we show that this latter result is an immediate consequence of a more general result, namely that the volume of coconvex bodies is strictly convex. This result itself follows from a classical elementary result about the concavity of the volume of convex bodies inscribed in the same cylinder.