A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue

We prove a Brunn-Minkowski-type inequality for the eigenvalue Λ of the Monge-Ampère operator: Λ-1/2n is concave in the class of C+2 domains in Rn endowed with Minkowski addition. The equality case is explicitly described too. The main device of the proof is a notion of addition for convex functions, called infimal convolution, which corresponds to the Minkowski addition of the graphs of the involved functions.