@article{b8c89dd59f0d4327956fd244517833f2,
title = "Small curvature concentration and Ricci flow smoothing",
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 which only depends on the initial almost Euclidean structure. As applications, we use the Ricci flows to study the diffeomorphism type of manifolds and the regularity of Gromov-Hausdorff limit of manifolds with small curvature concentration.",
keywords = "Gap theorems, Pseudolocality, Ricci flows",
author = "Chan, {Pak Yeung} and Eric Chen and Lee, {Man Chun}",
note = "Acknowledgments: The authors would like to thank Peter Topping for the interest in this work as well as Gilles Carron for pointing out the reference [9] and related results. The authors would also like to thank the referee for pointing out a mistake in the earlier version of this paper. P.-Y. Chan would like to thank Bennett Chow, Lei Ni and Jiaping Wang for continuous encouragement and support. E. Chen thanks Guofang Wei and Rugang Ye for their support. Part of this work was carried out while M.-C. Lee was working at the Department of Mathematics at Northwestern University as a Boas Assistant Professor and at the Department of Mathematics at University of Warwick as a Research Fellow, which he would like to thank for the hospitality. E. Chen was partially supported by an AMS–Simons Travel Grant. M.-C. Lee was partially supported by NSF grant DMS-1709894 and EPSRC grant number P/T019824/1.",
year = "2022",
month = may,
day = "15",
doi = "10.1016/j.jfa.2022.109420",
language = "English (US)",
volume = "282",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "10",
}