Logarithmic Brunn-Minkowski conjecture - Monge-Ampere equations, Gaussian density and convex geometry

06.03.2019 16:15 - 19:00

Karoly Böröczky (CEU & Renyi Institute)

The classical Minkowski problem asks for a the existence of a smooth closed convex hypersurface in R^n whose Gauss curvature is given as the function of the exterior unit normal, therefore it is a Monge-Ampere type equation on the sphere. The uniqueness of the solution up to translation follows from the Brunn-Minkowski inequality of convex bodies in R^n. The talk discusses a recent variant, the so-called logarithmic-Minkowski problem and the related logarithmic Brunn-Minkowski conjecture for origin symmetric convex bodies where the conjecture is also related to various conjectured properties of the Gaussian density.

M. Eichmair, Ch. Krattenthaler

Sky Lounge, 12. OG, OMP 1