Functional inequalities on path space of sub-Riemannian manifolds and applications
by Li-Juan Cheng, Erlend Grong and Anton Thalmaier
Abstract
For sub-Riemannian manifolds with a chosen complement, we first establish the derivative formula and integration by parts formula on path space with respect to a well-defined gradient operator. By using these formulae, we then show that upper and lower bounds of the horizontal Ricci curvature correspond to functional inequalities on path space analogous to what has been established in Riemannian geometry by Aaron Naber, such as gradient inequalities, log-Sobolev and Poincaré inequalities.
Nonlinear Analysis 210 (2021), 112387
https://doi.org/10.1016/j.na.2021.112387
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