Geometric inequalities for manifolds with Ricci curvature in the Kato class

Gilles Carron (1, 2)

1 Géométrie et analyse globale
2 LMJL - Laboratoire de Mathématiques Jean Leray

We obtain an 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, Betti number estimates for closed manifolds whose Ricci curvature is controlled in the Kato class.

Mots clés: Sobolev inequalities; Volume growth; Green kernel; Doob transform

Domaines: Géométrie différentielle [math.DG]

Gilles Carron. Geometric inequalities for manifolds with Ricci curvature in the Kato class. Annales de l'Institut Fourier, 2020, 69 (7), pp.3095-3167. ⟨10.5802/aif.3346⟩. ⟨hal-01441891⟩