Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in Carnot groups
Analysis of PDEs
2015-04-03 v1 Differential Geometry
Probability
Abstract
We prove an optimal reverse Poincar\'e inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.
Keywords
Cite
@article{arxiv.1504.00603,
title = {Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in Carnot groups},
author = {Fabrice Baudoin and Michel Bonnefont},
journal= {arXiv preprint arXiv:1504.00603},
year = {2015}
}