On the equality case in the Brunn-Minkowski inequality for the Monge-Ampère eigenvalue

Abstract

We characterize the equality case in the Brunn-Minkowski inequality for the Monge-Ampère eigenvalue of general bounded convex domains. This together with the author's previous work completely resolves a question raised by Salani (A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue. Adv. Math. 194 (2005)).

To appear in J. Spectr. Theory