Geometric inequalities for manifolds with Ricci curvature in the Kato class

Gilles Carron

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arXiv · 1612.03027

Geometric inequalities for manifolds with Ricci curvature in the Kato class

Gilles Carron

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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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Gilles Carron. 2016-12-09. Geometric inequalities for manifolds with Ricci curvature in the Kato class. https://arxiv.org/abs/1612.03027

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