On the volume of the convex hull of two convex bodies

G. Horváth, Ákos and Lángi, Zsolt (2014) On the volume of the convex hull of two convex bodies. Monatshefte für Mathematik, 174. pp. 219-229.

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Abstract

In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$-space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are translates, or reflected copies of each other about a common point or a hyperplane containing it. In particular, we give a proof of a related conjecture of Rogers and Shephard.

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