Convexity Seminar

Spherical Monge-Ampere-Type Equations and Brunn-Minkowski-Type Inequalities

Location: Warren Weaver Hall 1302

Date: Tuesday, February 3, 2026, 11 a.m.

Synopsis:

An equivalence connection between existence and uniqueness of solutions to spherical Monge-Ampere-type equations and sharp geometric inequalities of Brunn-Minkowski-type will be described. We start with the equivalence of the solution to the classical Minkowski problem and the classical Brunn-Minkowski inequality, and then explain that such an equivalence exists in general, by giving a general form of spherical Monge-Ampere-type equations for geometric measures arising from unsolved Minkowski-type problems and conjectured Brunn-Minkowski-type inequalities.