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arXiv · 1211.0221

Volume and distance comparison theorems for sub-Riemannian manifolds

Fabrice Baudoin·Michel Bonnefont·Nicola Garofalo·Isidro H. Munive
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Abstract

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}.

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Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo, Isidro H. Munive. 2014-07-30. Volume and distance comparison theorems for sub-Riemannian manifolds. https://arxiv.org/abs/1211.0221

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