Reverse Poincare inequalities, Isoperimetry, and Riesz transforms in Carnot groups

Published 2 Apr 2015 in math.AP, math.DG, and math.PR | (1504.00603v1)

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.

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