English

Small curvature concentration and Ricci flow smoothing

Differential Geometry 2022-02-08 v3

Abstract

We show that a complete Ricci flow of bounded curvature which begins from a manifold with a Ricci lower bound, local entropy bound, and small local scale-invariant integral curvature control will have global point-wise curvature control at positive times. As applications, we obtain under similar assumptions a compactness result and a gap theorem for complete noncompact manifolds with nonnegative Ricci Curvature.

Keywords

Cite

@article{arxiv.2102.12840,
  title  = {Small curvature concentration and Ricci flow smoothing},
  author = {Pak-Yeung Chan and Eric Chen and Man-Chun Lee},
  journal= {arXiv preprint arXiv:2102.12840},
  year   = {2022}
}

Comments

29 pages, reference updated, result added, minor mistakes fixed

R2 v1 2026-06-23T23:30:20.762Z