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• W178656816 abstract "This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic notions which have been applied to study sequences of submanifolds in Euclidean space: Hausdorff convergence of sets, flat convergence of integral currents, and weak convergence of varifolds. We next describe a variety of intrinsic notions of convergence which have been applied to study sequences of compact Riemannian manifolds: Gromov-Hausdorff convergence of metric spaces, convergence of metric measure spaces, intrinsic Flat convergence of integral current spaces, and ultralimits of metric spaces. We close with a speculative section addressing possible notions of intrinsic varifold convergence, convergence of Lorentzian manifolds and area convergence." @default.
• W178656816 created "2016-06-24" @default.
• W178656816 creator A5022269955 @default.
• W178656816 date "2012-01-01" @default.
• W178656816 modified "2023-09-26" @default.
• W178656816 title "How Riemannian Manifolds Converge" @default.
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• W178656816 doi "https://doi.org/10.1007/978-3-0348-0257-4_4" @default.
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