The Li-Yau inequality and applications under a curvature-dimension condition - Université Claude Bernard Lyon 1 Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

The Li-Yau inequality and applications under a curvature-dimension condition

Résumé

We prove a global Li-Yau inequality for a general Markov semigroup under a curvature-dimension condition. This inequality is stronger than all classical Li-Yau type inequalities known to us. On a Riemannian manifold, it is equivalent to a new parabolic Harnack inequality, both in negative and positive curvature, giving new subsequents bounds on the heat kernel of the semigroup. Under positive curvature we moreover reach ultracontractive bounds by a direct and robust method.
Fichier principal
Vignette du fichier
HAL-li-yau-2.pdf (338.82 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01094046 , version 1 (11-12-2014)
hal-01094046 , version 2 (31-03-2015)
hal-01094046 , version 3 (21-07-2016)

Identifiants

Citer

Dominique Bakry, François Bolley, Ivan Gentil. The Li-Yau inequality and applications under a curvature-dimension condition. 2014. ⟨hal-01094046v2⟩
660 Consultations
339 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More