Stochastic analysis on sub-Riemannian manifolds with transverse symmetries

• Fabrice Baudoin ^[1]
  1. [1] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 1, 2017, págs. 56-81
• Idioma: inglés
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• Resumen

  • 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–Weitzenböck 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.