2 citations · 4 across the 7 of their papers we have counts for
8 papers
Some obstructions to contraction theorems on the half-sphere
Max Fathi, Matthieu Fradelizi, Nathael Gozlan +1
Caffarelli's contraction theorem states that probability measures with uniformly logconcave densities on R d can be realized as the image of a standard Gaussian measure by a global…
Transport-entropy forms of direct and Converseblaschke-Santal{ó} inequalities
Matthieu Fradelizi, Nathael Gozlan, Shay Sadovsky +1
We explore alternative functional or transport-entropy formulations of the Blaschke-Santal{ó} inequality and of its conjectured counterpart due to Mahler. In particular, we obtain…
A conformal geometric point of view on the Caffarelli-Kohn-Nirenberg inequality
Louis Dupaigne, Ivan Gentil, Simon Zugmeyer
We are interested in the Caffarelli-Kohn-Nirenberg inequality (CKN in short), introduced by these authors in 1984. We explain why the CKN inequality can be viewed as a Sobolev ineq…
Transport proofs of some functional inverse Santal{ó} inequalities
Matthieu Fradelizi, Nathael Gozlan, Simon Zugmeyer
In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{ó} inequalities follow from Entropy-Transport ineq…
Sobolev's inequality under a curvature-dimension condition
Louis Dupaigne, Ivan Gentil, Simon Zugmeyer
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to…
Entropy flows and functional inequalities in convex sets
Simon Zugmeyer
We revisit entropy methods to prove new sharp trace logarithmic Sobolev and sharp Gagliardo-Nirenberg-Sobolev inequalities on the half space, with a focus on the entropy inequality…