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

Zuohai Jiang; Lingling Kong; Shicheng Xu

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arXiv · 2205.00373

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

Zuohai Jiang·Lingling Kong·Shicheng Xu

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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 $C^{1,\alpha}$-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 $C^{1,\alpha}$ limit spaces.

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Zuohai Jiang, Lingling Kong, Shicheng Xu. 2022-05-01. Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I. https://arxiv.org/abs/2205.00373

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