BAUDOIN, Fabrice; BONNEFONT, Michel

doi:10.1016/j.na.2015.06.025

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BAUDOIN, Fabrice
Department of Mathematics

BONNEFONT, Michel
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Nonlinear Analysis: Theory, Methods and Applications. 2015, vol. 126, p. 159-169

Elsevier

Résumé en anglais

We study Bakry-Emery type estimates for the Laplace-Beltrami operator of a totally geodesic foliation. In particular, we are interested in situations for which the Γ2 operator may not be bounded from below but the horizontal Bakry-Emery curvature is. As we prove it, under a bracket generating condition, this weaker condition is enough to imply several functional inequalities for the heat semigroup including the Wang-Harnack inequality and the log-Sobolev inequality. We also prove that, under proper additional assumptions, the generalized curvature dimension inequality introduced by Baudoin-Garofalo is uniformly satisfied for a family of Riemannian metrics that converge to the sub-Riemannian one.< Réduire