We prove a Brunn–Minkowski-type inequality for the eigenvalue of the Monge–Ampère operator. 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.
A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue / P. SALANI. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 194:(2005), pp. 67-86. [10.1016/j.aim.2004.05.011]
A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue
SALANI, PAOLO
2005
Abstract
We prove a Brunn–Minkowski-type inequality for the eigenvalue of the Monge–Ampère operator. 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.
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