Thèse soutenue

Auteur / Autrice : Van Hoang Nguyen
Direction : Dario Cordero-Erausquin
Type : Thèse de doctorat
Discipline(s) : Mathématiques
Date : Soutenance en 2013
Etablissement(s) : Paris 6


FR  |  

Chapter 1, we prove a quantitative version of the Shannon-Stam’s entropy inequality. In application of this result, we show that the KLS’s conjecture implies the hyperplane conjecture. Chapter 2, we use the Hormander L^2 method to prove the generalizations of the dimensional variance inequality obtained recently by Bobkov and Ledoux. Using these generalizations, we obtain the reverve Holder inequalities, the Brascamp-Lieb inequality for the log-concave density, and the weighted Brascamp-Lieb inequality for the convex measure. Chapter 3, we use the methode of optimal transport to prove a family of the sharp weighted Sobolev and sharp weighted Gagliardo-Nirenberg inequalities on the half-space. Using the sharp weighted Sobolev inequalities with the method of reduction of the dimension, we obtain and generalize the sharp Gagliardo-Nirenberg inequalities on the euclidean space.