English

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