Volume and distance comparison theorems for sub-Riemannian manifolds

Fabrice Baudoin (1) , Michel Bonnefont (2) , Nicola Garofalo , Isidro H. Munive

1 Department of Mathematics
2 IMB - Institut de Mathématiques de Bordeaux

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 dimension inequality introduced by the first and the third author in \cite{BG1} 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 \cite{BG1}.

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo, Isidro H. Munive. Volume and distance comparison theorems for sub-Riemannian manifolds. Journal of Functional Analysis, 2014, 141 (11), pp.3919-3924. ⟨hal-00779393⟩