[en] We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. ItÃ´'s formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng's type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group.

University of Luxembourg - UL

R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton