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Article Dans Une Revue Séminaire de Théorie Spectrale et Géométrie Année : 2017

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

Théorie spectrale et géométrie

François Fillastre

Résumé

The theory of coconvex bodies was formalized by A. Khovanski˘ı and V. Timorin in [4]. It has fascinating relations with the classical theory of convex bodies, as well as applications to Lorentzian geometry. In a recent preprint [5], 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.

Dates et versions

hal-03793212 , version 1 (14-10-2022)

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Citer

François Fillastre. A short elementary proof of reversed Brunn–Minkowski inequality for coconvex bodies. Séminaire de Théorie Spectrale et Géométrie, 2017, 34, pp.93-96. ⟨10.5802/tsg.356⟩. ⟨hal-03793212⟩
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