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arXiv · 1601.08191

Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

Xianzhe Dai·Guofang Wei·Zhenlei Zhang
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Abstract

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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Xianzhe Dai, Guofang Wei, Zhenlei Zhang. 2016-01-29. Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds. https://arxiv.org/abs/1601.08191

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