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.
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