Ricci Flow Under Kato-Type Curvature Lower Bound

In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type curvature lower bound. As an application, we prove that any compact three-dimensional non-collapsed strong Kato limit space is homeomorphic to a smooth manifold. Moreover, sim...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 34; no. 3
Main Author Lee, Man-Chun
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2024
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Curvature
Differential Geometry
Dynamical Systems and Ergodic Theory
Flow stability
Fourier Analysis
Global Analysis and Analysis on Manifolds
Lower bounds
Mathematics
Mathematics and Statistics
Kato-type lower bound
Primary: 53E20
Stability
Ricci flow smoothing
53C21
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Summary:In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type curvature lower bound. As an application, we prove that any compact three-dimensional non-collapsed strong Kato limit space is homeomorphic to a smooth manifold. Moreover, similar result also holds in higher dimension under stronger curvature condition. We also use the Ricci flow smoothing to study stability problem in scalar curvature geometry.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01522-4