Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I

2022/05/01 by Zuohai Jiang, Jiang, Zuohai, Lingling Kong +3
Mathematics · Medicine · #5324 #53C20 #53C21 #53C23 #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2205.00373

openalex publication_date 2022/05/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We extend Cheeger-Gromov's and Anderson's convergence theorems to regular limit spaces of manifolds with bounded Ricci curvature and local covering geometry, by establishing the C^1,α-regularities that are the best one may expect on those Ricci-limit spaces. As an application we prove an optimal generalization of Fukaya's fibration theorem on collapsed manifolds with bounded Ricci curvature, which also improves the original version to C^1,α limit spaces.

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