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Volume and distance comparison theorems for sub-Riemannian manifolds

Authors
  • Baudoin, Fabrice
  • Bonnefont, Michel
  • Garofalo, Nicola
  • Munive, Isidro H.
Type
Preprint
Publication Date
Jul 30, 2014
Submission Date
Nov 01, 2012
Identifiers
arXiv ID: 1211.0221
Source
arXiv
License
Yellow
External links

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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