Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds

By X. Dai, Guofang Wei, Zhenlei Zhang. 2016

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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.

Subfields: Applied Mathematics, Geometry and Topology, Surgery

View Paper: https://www.semanticscholar.org/paper/0714896784fe8b9e94a73a4d4930d1b20fd9fae3