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Ricci Flow and Gromov Almost Flat Manifolds

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arxiv 2203.05107 v1 pith:7KZ3PICM submitted 2022-03-10 math.DG

Eric Chen , Guofang Wei , Rugang Ye This is my paper · ORCID
classification math.DG
keywords theoremalmostconditionflatflowgromovgromov--ruhmanifolds
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abstract

We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov--Ruh Theorem. In our theorem, the condition $diam^2 |K| \leq \epsilon_n$ in the Gromov--Ruh Theorem is replaced by the substantially weaker condition $\|Rm\|_{n/2}$ $ C_S^2 \leq \varepsilon_n$.

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  1. A note on a diffeomorphism criterion via long-time Ricci flow

    math.DG 2025-09 conditional novelty 6.0 of 10

    A long-time Ricci flow with Ric ≥ -ψ/t and sufficiently large injectivity radius forces the manifold to be diffeomorphic to R^n, improving dimension-4 small-curvature-concentration results.

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