On the regular-convexity of Ricci shrinker limit spaces
Differential Geometry
2020-05-28 v2
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.
Keywords
Cite
@article{arxiv.1809.04386,
title = {On the regular-convexity of Ricci shrinker limit spaces},
author = {Shaosai Huang and Yu Li and Bing Wang},
journal= {arXiv preprint arXiv:1809.04386},
year = {2020}
}
Comments
revised version, to appear in J. Reine Angew. Math