BAUDOIN, Fabrice; BONNEFONT, Michel; GAROFALO, Nicola

doi:10.1007/s00208-013-0961-y

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BAUDOIN, Fabrice
Department of Mathematics

BONNEFONT, Michel
Institut de Mathématiques de Bordeaux [IMB]

GAROFALO, Nicola

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Mathematische Annalen. 2014, vol. 358, n° 3-4, p. 833-860

Springer Verlag

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Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $\mu$. We show that if $L$ satisfies, with a non negative curvature parameter, the generalized curvature inequality introduced by the first and third named authors in \cite{BG}, then the following properties hold: 1 The volume doubling property; 2 The Poincaré inequality; 3 The parabolic Harnack inequality. The key ingredient is the study of dimensional reverse log-Sobolev inequalities for the heat semigroup and corresponding non-linear reverse Harnack type inequalities. Our results apply in particular to all Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and to wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative.< Leer menos

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A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

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