Reverse Poincaré inequalities, isoperimetry, and Riesz transforms in Carnot groups. (January 2016) - Baudoin, Fabrice; Bonnefont, Michel
Abstract: We prove an optimal reverse Poincaré 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.