4 papers
Godbersen's conjecture and the -Rogers-Shephard inequality
Jan Kotrbatý, Mohamed A. Mouamine
We prove that the mixed volume of a convex body with its reflection about the origin is maximized by simplices. This confirms a conjecture of C. Godbersen from 1938 and refines the…
Additive Kinematic Formulas for Functional Minkowski Vectors
Mohamed A. Mouamine
We establish an additive kinematic formula for the functional Minkowski vectors using mixed Monge-Ampère measures. These vectors, recently introduced and characterized by the auth…
The Vectorial Hadwiger Theorem on Convex Functions
Mohamed A. Mouamine, Fabian Mussnig
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently i…
A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
Mohamed A. Mouamine, Fabian Mussnig
A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant,…