Limits of manifolds with a Kato bound on the Ricci curvature. II

2022/05/04 by Gilles Carron, Carron, Gilles, Ilaria Mondello +3 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2205.01956

openalex publication_date 2022/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that metric measure spaces obtained as limits of closed Riemannian manifolds with Ricci curvature satisfying a uniform Kato bound are rectifiable. In the case of a non-collapsing assumption and a strong Kato bound, we additionally show that for any α∈ (0,1) the regular part of the space lies in an open set with the structure of a C^α-manifold.

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• Mosco-convergence of Cheeger energies on varying spaces satisfying curvature dimension conditions
• Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization

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