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On the regular-convexity of Ricci shrinker limit spaces

Shaosai Huang, Yu Li and Bing Wang


In this paper we study the structure of the pointed-Gromov–Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger–Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any non-collapsing Ricci shrinker limit space is strongly convex, inspired by Colding–Naber’s original idea of parabolic smoothing of the distance functions.

Funding source: National Science Foundation

Award Identifier / Grant number: DMS-1510401

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11971452

Funding statement: The third-named author was partially supported by NSF grant DMS-1510401, as well as the General Program of the National Natural Science Foundation of China (Grant No. 11971452).


We would like to thank the anonymous referees for several valuable comments that help improve the exposition of the paper.


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Received: 2019-01-30
Revised: 2020-04-22
Published Online: 2020-07-11
Published in Print: 2021-02-01

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