On the regular-convexity of Ricci shrinker limit spaces

2018/09/12 by Shaosai Huang, Yu Li, Huang, Shaosai +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1809.04386

openalex publication_date 2018/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

Related

• Geometric Structure of Ends of Ricci Shrinkers
• Ends of (singular) Ricci shrinkers
• Weak Ricci curvature bounds for Ricci shrinkers
• The Rigidity of Ricci shrinkers of dimension four
• Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers