The geometry of Markov diffusion generators
Michel Ledoux (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Michel Ledoux (2000)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Michel Ledoux (1999)
Séminaire de probabilités de Strasbourg
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Ivan Gentil (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.
L. Saloff-Coste (1994)
Colloquium Mathematicae
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Guangyue Huang, Fanqi Zeng (2016)
Studia Mathematica
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We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.
Franck Barthe (2001)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Ernst Heintze, Hermann Karcher (1978)
Annales scientifiques de l'École Normale Supérieure
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