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Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

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arxiv 1601.08191 v4 pith:2HK37G2H submitted 2016-01-29 math.DG

Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

classification math.DG
keywords estimateintegralricciboundsconstantcurvaturelocalsobolev
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We obtain a local Sobolev constant estimate for integral Ricci curvature, which enables us to extend several important tools such as the maximal principle, the gradient estimate, the heat kernel estimate and the $L^2$ Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.

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