Volume and distance comparison theorems for sub-Riemannian manifolds

摘要

In this paper we study global distance estimates and uniform local volume estimates in a large class of sub-Riemannian manifolds. Our main device is the generalized curvature di-mension inequality introduced by the first and the third au-thor in [3]and its use to obtain sharp inequalities for solutions of the sub-Riemannian heat equation. As a consequence, we obtain a Gromov type precompactness theorem for the class of sub-Riemannian manifolds whose generalized Ricci curvature is bounded from below in the sense of [3].