A New Proof of the Gromov's Theorem on Almost Flat Manifolds

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arxiv 1906.03377 v3 pith:VZNXAOLJ submitted 2019-06-08 math.DG

Xiaochun Rong This is my paper · ORCID

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keywords proofalmostflatgromovmanifoldstheoremdimensiongive

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We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.

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On the non-collapsed RCD spaces with local bounded covering geometry
math.DG 2024-12 conditional novelty 7.0 of 10

Small-diameter non-collapsed RCD spaces with locally non-collapsing universal covers are biHolder equivalent to infranil-manifolds, and collapsing RCD sequences fiber over their limits with infranil fibers.