The (B) conjecture for uniform measures in the plane

Abstract

We prove that for any two centrally-symmetric convex shapes $K,L\subset {\mathbb{R}}^2$, the function $t\mapsto |e^{t}K\cap L|$ is log-concave. This extends a result of Cordero-Erausquin, Fradelizi and Maurey in the two dimensional case. Possible relaxations of the condition of symmetry are discussed.

10 pages