Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I
by Erlend Grong and Anton Thalmaier

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

The paper is available here:

Erlend Grong
Anton Thalmaier

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