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arXiv · 1809.04386

On the regular-convexity of Ricci shrinker limit spaces

Shaosai Huang·Yu Li·Bing Wang
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Abstract

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 Ricci shrinker limit space is convex, inspired by Colding-Naber's original idea of parabolic smoothing of the distance functions.

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Shaosai Huang, Yu Li, Bing Wang. 2018-09-12. On the regular-convexity of Ricci shrinker limit spaces. https://arxiv.org/abs/1809.04386

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