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arXiv · 1412.3777

Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation

Fabrice Baudoin·Michel Bonnefont
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Abstract

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 $\Gamma_2$ 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.

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Fabrice Baudoin, Michel Bonnefont. 2014-12-11. Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation. https://arxiv.org/abs/1412.3777

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