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 convexbodies, 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.