Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I
by Erlend Grong and Anton Thalmaier
Abstract
We give a generalized curvature-dimension inequality connecting the
geometry of sub-Riemannian manifolds with the properties of its
sub-Laplacian. This inequality is valid on a large class of
sub-Riemannian manifolds obtained from Riemannian foliations. We
give a geometric interpretation of the invariants involved in the
inequality. Using this inequality, we obtain a lower bound for the
eigenvalues of the sub-Laplacian. This inequality also lays the foundation for
proving several powerful results in Part II.
Math. Zeitschrift 282 (2016) 99-130
http://dx.doi.org/10.1007/s00209-015-1534-4
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