STOCHASTIC ANALYSIS ON SUB-RIEMANNIAN MANIFOLDS WITH TRANSVERSE SYMMETRIES

• 成果类型: Article
• 署名作者: Baudoin, Fabrice
• 署名单位: Purdue University System; Purdue University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP964
• 发表日期: 2017
• 页码: 56-81
• 关键词: curvature-dimension inequality; hypoelliptic heat-kernel; heisenberg-group; Operators; gradient; geometry; bundles

摘要

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