Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds
Differential Geometry
2017-12-04 v4
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 Hessian estimate to manifolds with integral Ricci lower bounds, without the non-collapsing conditions.
Keywords
Cite
@article{arxiv.1601.08191,
title = {Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds},
author = {Xianzhe Dai and Guofang Wei and Zhenlei Zhang},
journal= {arXiv preprint arXiv:1601.08191},
year = {2017}
}
Comments
typos corrected, to appear in Advances in Mathematics