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

Abstract

Using the curvature-dimension inequality proved in Part~I, we look at consequences of this inequality in terms of the interaction between the sub-Riemannian geometry and the heat semigroup $P_t$ corresponding to the sub-Laplacian. We give bounds for the gradient, entropy, a Poincaré inequality and a Li-Yau type inequality. These results require that the gradient of $P_{t}f$ remains uniformly bounded whenever the gradient of $f$ is bounded and we give several sufficient conditions for this to hold.

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

References in corpus (2)

• Generalized Curvature Condition for Subelliptic Diffusion Processes
• Transverse Weitzenböck formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves

Cited by in corpus (1)

• Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus