English

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 L2L^2 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