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 in:The Journal of geometric analysis 2023-09, Vol.33 (9), Article 285
Main Authors: Wu, Guoqiang, Wu, Jia-Yong
Format: Article
Language:English
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
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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