Small curvature concentration and Ricci flow smoothing

Pak Yeung Chan, Eric Chen, Man Chun Lee

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number109420
JournalJournal of Functional Analysis
Volume282
Issue number10
DOIs
StatePublished - May 15 2022
Externally publishedYes

Keywords

  • Gap theorems
  • Pseudolocality
  • Ricci flows

ASJC Scopus subject areas

  • Analysis

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