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Journal Articles Annales de l'Institut Fourier Year : 2020

Geometric inequalities for manifolds with Ricci curvature in the Kato class

Gilles Carron

Abstract

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.
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hal-01441891 , version 1 (27-05-2024)

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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⟩
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