Shrinkers with Curvature-Pinching Conditions are Compact

In this paper, we give various curvature-pinching conditions such that shrinkers are compact. On one hand, we prove that shrinkers with positive Ricci curvature are compact when they have bounded curvature and certain curvature-pinching conditions. On the other hand, we prove that shrinkers with cer...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 9
Main Authors Wu, Guoqiang, Wu, Jia-Yong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2023
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Convex and Discrete Geometry
Curvature
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Eigenvalues pinching
Classification
53C21
Secondary 53C20
Gradient shrinking Ricci soliton
Compact manifold
Primary 53C25
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Summary:In this paper, we give various curvature-pinching conditions such that shrinkers are compact. On one hand, we prove that shrinkers with positive Ricci curvature are compact when they have bounded curvature and certain curvature-pinching conditions. On the other hand, we prove that shrinkers with certain asymptotically nonnegative sectional curvature are compact. As applications, some related classifications of shrinkers are provided.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01352-4