On gradient estimates of the heat semigroups on step-two Carnot groups
Abstract
In this work, we give a sufficient condition for a step-two Carnot group to satisfy the quasi Bakry-Émery curvature condition. As an application, we establish the gradient estimate for the heat semigroup on the free step-two Carnot group with three generators N3,2. Moreover, high order gradient estimates and the Riemannian counterparts are also deduced under an extra condition.
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