Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation

Abstract

We develop a Malliavin calculus on the horizontal path space of a totally geodesic Riemannian foliation. As a first application, under suitable assumptions, we prove a log-Sobolev inequality for a natural one-parameter family of infinite-dimensional Ornstein-Uhlenbeck type operators. As a second application, we obtain concentration and tail estimates for the horizontal Brownian motion of the foliation.

References in corpus (1)

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

Cited by in corpus (5)

• Sub-Riemannian Ricci curvature via generalized Gamma $z$ calculus
• Harnack inequalities on totally geodesic foliations with transverse Ricci flow
• Functional inequalities on path space of sub-Riemannian manifolds and applications
• Eells-Sampson type theorems for subelliptic harmonic maps from sub-Riemannian manifolds
• Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifold