References of "Baudoin, Fabrice"
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See detailRadial processes for sub-Riemannian Brownian motions and applications
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa et al

in Electronic Journal of Probability (2020), 25(paper no. 97), 1-17

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating ... [more ▼]

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô'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. [less ▲]

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See detailSub-Laplacian comparison theorems on totally geodesic Riemannian foliations
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa et al

in Calculus of Variations and Partial Differential Equations (2019), 58:130(4), 1-38

We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical ... [more ▼]

We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations. [less ▲]

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