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- W2964055642 abstract "Abstract In this paper we study collapsing sequences <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>M</m:mi> <m:mi>i</m:mi> </m:msub> <m:mover> <m:mo>→</m:mo> <m:mo>GH</m:mo> </m:mover> <m:mi>X</m:mi> </m:mrow> </m:math> M_{i}xrightarrow{rm GH}X of Riemannian manifolds with curvature bounded or bounded away from a controlled subset. We introduce a structure over X which in an appropriate sense is dual to the N -structure of Cheeger, Fukaya and Gromov. As opposed to the N -structure, which live over the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>M</m:mi> <m:mi>i</m:mi> </m:msub> </m:math> {M_{i}} themselves, this structure lives over X and allows for a convenient notion of global convergence as well as the appropriate background structure for doing analysis on X . This structure is new even in the case of uniformly bounded curvature and as an application we give a generalization of Gromov’s Almost Flat Theorem and prove new Ricci pinching theorems which extend those known in the noncollapsed setting. There are also interesting topological consequences to the structure." @default.
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- W2964055642 date "2016-03-10" @default.
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- W2964055642 title "Geometric structures of collapsing Riemannian manifolds II" @default.
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- W2964055642 doi "https://doi.org/10.1515/crelle-2015-0082" @default.
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