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math.DS2017★ 2 cited
Duality of Caustics in Minkowski Billiards
Shiri Artstein-Avidan, Dan Itzhak Florentin, Yaron Ostrover +1
In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth centrally symmetric and strictly convex body ,…
math.FA2017
Functional Brunn-Minkowski Inequalities Induced by Polarity
Shiri Artstein-Avidan, Dan I. Florentin, Alexander Segal
We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical i…