Speaker: Rotem Assouline (Weizmann Institute)

Title: Brunn Minkowski inequality for horocycles

Abstract:
The Minkowski average of two sets on a Riemannian manifold can be defined by replacing straight lines with geodesics. The Brunn Minkowski inequality is then equivalent to nonnegative Ricci curvature. We propose a generalization of this operation in which geodesics are replaced by an arbitrary family of curves. We show that horocycles in the hyperbolic plane satisfy the Brunn Minkowski inequality, in stark contrast to geodesics. Our main tool is needle decomposition. Joint work with Bo'az Klartag.

Zoom link: https://huji.zoom.us/j/88091075385?pwd=Q2IxRDBiYVY5Z2dFSEMvNjRMcWdYZz09