Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part I

2014/08/28 by Erlend Grong, Grong, Erlend, Anton Thalmaier +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.48550/arxiv.1408.6873

31 pages, Part 1 of 2. To appear in Mathematische Zeitschrift

arxiv created 2015/07/29 · arxiv updated 2015/07/30

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.

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