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math.DG2022
Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits
Zuohai Jiang, Lingling Kong, Shicheng Xu
It is known that a closed collapsed Riemannian -manifold of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of C…
math.DG2022
Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound
Lina Chen, Shicheng Xu
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $…
math.DG2022
Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I
Zuohai Jiang, Lingling Kong, Shicheng Xu
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…