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

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), no. 1, 67–86.).