Stochastic analysis on sub-Riemannian manifolds with transverse symmetries

Abstract

We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions. The results are new even in the case of the Heisenberg group which is the simplest example of a sub-Riemannian manifold with transverse symmetries.

References in corpus (2)

• Formulae for the derivatives of heat semigroups
• On gradient bounds for the heat kernel on the Heisenberg group

Cited by in corpus (1)

• Transverse Weitzenböck formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves