Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations
Fabrice Baudoin
TL;DR
This paper surveys recent advances in the geometric analysis of hypoelliptic operators on totally geodesic Riemannian foliations and introduces new applications to hypocoercive estimates for Kolmogorov-type operators.
Contribution
It provides a comprehensive overview of recent results and introduces novel applications in hypocoercivity for Kolmogorov operators on Riemannian foliations.
Findings
Recent results on hypoelliptic diffusion operators on Riemannian foliations
New applications to hypocoercive estimates for Kolmogorov operators
Enhanced understanding of geometric analysis in hypoelliptic contexts
Abstract
These notes are the basis of a course given at the Institut Henri Poincare in September 2014. We survey some recent results related to the geometric analysis of hypoelliptic diffusion operators on totally geodesic Riemannian foliations. We also give new applications to the study of hypocoercive estimates for Kolmogorov type operators.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Advanced Mathematical Modeling in Engineering