  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.

Differential Geometry