As on arXiv
Abstract
In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type lower bound. As an application, we prove that compact three dimensional non-collapsed strong Kato limit space is homeomorphic to a smooth manifold. The result also holds in higher dimension under uniform strong Kato lower bound of 1-isotropic curvature. We also use the Ricci flow smoothing to study stability problem in scalar curvature geometry.
Comments: printing mistakes corrected, proof expanded, symbols unified, 21 pages
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow
Topics (Non)collapsing, 3-manifolds, Scalar curvature · Shared terms “curvature lower”, “lower bound”
-
Gap Theorem on Riemannian manifolds using Ricci flow
Topics (Non)collapsing, 3-manifolds · Same author Man-Chun Lee · Shared terms “existence theory”
-
Uniqueness of Ricci flow with scaling invariant estimates
Topics (Non)collapsing, 3-manifolds, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “collapsed”
-
Spaces with distributional scalar curvature bounded from below: Optimal regularity and positive mass
Topics Scalar curvature · Same author Man-Chun Lee · Shared terms “flow smoothing”, “curvature lower”, “lower bound”
-
Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition
Topics Scalar curvature, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “existence theory”, “curvature lower”, “flow smoothing”
-
Rigidity of Lipschitz map using harmonic map heat flow
Topics Scalar curvature, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “curvature lower”, “curvature geometry”, “lower bound”
-
Higher-dimensional flying wing Steady Ricci Solitons
Topics (Non)collapsing, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “flow smoothing”, “collapsed”
-
Manifolds with small curvature concentration
Topics Scalar curvature · Same author Man-Chun Lee · Shared terms “lower bound”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 9B.3Collapsing and Noncollapsing
Injectivity radius bounds from volume, collapsing examples, and the definition Perelman needs.
- 12A.4κ-Noncollapsing
The theorem that excludes the cigar.
- 12A.8Local Noncollapsing from the Reduced Volume
Perelman's §§7.3 and 8: noncollapsing that needs only local curvature control, the small-and-large-vector split, the maximum principle for the reduced distance, and the form that survives surgery.