  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.
