Limits of manifolds with a Kato bound on the Ricci curvature
Copyright policy )Limits of manifolds with a Kato bound on the Ricci curvature
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 \(\alpha \in (0,1)\) the regular part of the space lies in an open set with the structure of a \(C^\alpha\)-manifold.
Mathematics - Differential Geometry, Dirichlet forms, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, Gromov–Hausdorff convergence, rectifiability, Heat and other parabolic equation methods for PDEs on manifolds, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, volume convergence, Gromov-Hausdorff convergence, Ricci curvature, Differential Geometry (math.DG), FOS: Mathematics, Kato class, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
Mathematics - Differential Geometry, Dirichlet forms, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, Gromov–Hausdorff convergence, rectifiability, Heat and other parabolic equation methods for PDEs on manifolds, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, volume convergence, Gromov-Hausdorff convergence, Ricci curvature, Differential Geometry (math.DG), FOS: Mathematics, Kato class, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
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