Volume and distance comparison theorems for sub-Riemannian manifolds

TY - JOUR

T1 - Volume and distance comparison theorems for sub-Riemannian manifolds

AU - Baudoin, Fabrice

AU - Bonnefont, Michel

AU - Garofalo, Nicola

AU - Munive, Isidro H.

N1 - Publisher Copyright: © 2014 Elsevier Inc.

PY - 2014/11/20

Y1 - 2014/11/20

N2 - 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 [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].

AB - 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 [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].

KW - Heat semigroup

KW - Sub-Riemannian manifold

KW - Volume comparison theorem

UR - https://www.scopus.com/pages/publications/84955205634

U2 - 10.1016/j.jfa.2014.07.030

DO - 10.1016/j.jfa.2014.07.030

M3 - Journal article

AN - SCOPUS:84955205634

SN - 0022-1236

VL - 267

SP - 2005

EP - 2027

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -