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arXiv · 1711.04272

A short elementary proof of reversed Brunn--Minkowski inequality for coconvex bodies

François Fillastre
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Abstract

The theory of coconvex bodies was formalized by A.~Khovanski{\u\i} and V.~Timorin in \cite{KT}. It has fascinating relations with the classical theory of convex bodies, as well as applications to Lorentzian geometry. In a recent preprint \cite{schnei2}, 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.

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François Fillastre. 2017-11-12. A short elementary proof of reversed Brunn--Minkowski inequality for coconvex bodies. https://arxiv.org/abs/1711.04272

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