Stochastic analysis on sub-Riemannian manifolds with transverse\n symmetries

2014/02/18 by Fabrice Baudoin, Baudoin, Fabrice · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1402.4490

Abstract

We prove a geometrically meaningful stochastic representation of the\nderivative of the heat semigroup on sub-Riemannian manifolds with tranverse\nsymmetries. This representation is obtained from the study of\nBochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a\nconsequence, we prove new hypoelliptic heat semigroup gradient bounds under\nnatural global geometric conditions. The results are new even in the case of\nthe Heisenberg group which is the simplest example of a sub-Riemannian manifold\nwith transverse symmetries.\n

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