Li–Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class
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We show that a heat kernel estimate holds based on a Kato-class condition for the negative part of Ricci curvature. This is a generalization of results based on \(L^p\)-bounds on the Ricci curvature. We also establish bounds on the first Betti number.
KeywordsHeat kernel Ricci curvature Kato class
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