Geometric inequalities for manifolds with Ricci curvature in the Kato class
Annales de l'Institut Fourier, Volume 69 (2019) no. 7, pp. 3095-3167.

We obtain Euclidean volume growth results for complete Riemannian manifolds satisfying a Euclidean Sobolev inequality and a spectral type condition on the Ricci curvature. We also obtain eigenvalue estimates, heat kernel estimates, and Betti number estimates for closed manifolds whose Ricci curvature is controlled in the Kato class.

On démontre qu’une variété riemannienne complète vérifiant une inégalité de Sobolev euclidienne et dont la courbure de Ricci est petite dans une classe de Kato et à croissance euclidienne du volume. On obtient aussi des estimations spectrales, du noyau de la chaleur et du premier nombre de Betti des variétés riemanniennes compactes dont la courbure de Ricci est controlée dans une classe de Kato.

Published online:
DOI: 10.5802/aif.3346
Classification: 53C21, 58J35, 58C40, 58J50
Keywords: Sobolev inequalities, volume growth, Green kernel, Doob transform
Mot clés : Inégalité de Sobolev, croissance du volume, noyau de Green, transformée de Doob
Carron, Gilles 1

1 Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, CNRS École Centrale de Nantes 2 rue de la Houssinière B.P. 92208 44322 Nantes Cedex 3 (France)
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Carron, Gilles. Geometric inequalities for manifolds with Ricci curvature in the Kato class. Annales de l'Institut Fourier, Volume 69 (2019) no. 7, pp. 3095-3167. doi : 10.5802/aif.3346. http://www.numdam.org/articles/10.5802/aif.3346/

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