The problem of q-moment measures via optimal transportation
Báo cáo viên: Huỳnh Khanh (Viện Toán học)

Thời gian: 14h Thứ 5, ngày 28/01/2021

Địa điểm: P507 nhà A6 hoặc online qua link


Tóm tắt: Motivated by a recent result in convex geometry on the existence of affine hemispheres of elliptic type, q-moment measures are studied by Klartag in 2017, by using a variational method requiring to minimize a functional among convex functions, which is studied using the Borell-Brascamp-Lieb inequality. q-moment measures are variant case the moment measures of Berman and Berndtsson in their work on Kahler-Einstein metrics in toric manifolds; Cordero-Erausquin and Klartag extended the study of Berman and Berndtsson in 2015 presenting a functional version of the classical Minkowski problem or the logarithmic Minkowski problem and providing a variational characterization... In this talk, we present a new approach for the problem of q-moment measures that its ideas coming from theory of optimal transport, replacing functional inequalities techniques with ideas from optimal transport. The variational problem in this new approach becomes the minimization of a local functional and a transport cost among probability measures with finite first momentum. (based on a joint work with Filippo Santambrogio -- ICJ, Lyon).