Back to Search
Start Over
Curvature-dimension estimates for the Laplace–Beltrami operator of a totally geodesic foliation.
- Source :
-
Nonlinear Analysis . Oct2015, Vol. 126, p159-169. 11p. - Publication Year :
- 2015
-
Abstract
- We study Bakry-Émery type estimates for the Laplace–Beltrami operator of a totally geodesic foliation. In particular, we are interested in situations for which the Γ 2 operator may not be bounded from below but the horizontal Bakry-Émery 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 and Garofalo (2015) is uniformly satisfied for a family of Riemannian metrics that converge to the sub-Riemannian one. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 126
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 109089437
- Full Text :
- https://doi.org/10.1016/j.na.2015.06.025