The Annals of Probability
- Ann. Probab.
- Volume 45, Number 1 (2017), 56-81.
Stochastic analysis on sub-Riemannian manifolds with transverse symmetries
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–Weitzenböck 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.
Ann. Probab., Volume 45, Number 1 (2017), 56-81.
Received: February 2014
Revised: June 2014
First available in Project Euclid: 26 January 2017
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Baudoin, Fabrice. Stochastic analysis on sub-Riemannian manifolds with transverse symmetries. Ann. Probab. 45 (2017), no. 1, 56--81. doi:10.1214/14-AOP964. https://projecteuclid.org/euclid.aop/1485421328