Ricci Flow and Gromov Almost Flat Manifolds

2022/03/10 by Eric Chen, Chen, Eric, Guofang Wei +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C20 #msc:53C21 #msc:53E20

paper · pdf · doi:10.48550/arxiv.2203.05107

arxiv created 2022/03/10 · arxiv updated 2022/03/11

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 diam² |K| ≤ ε_n in the Gromov--Ruh Theorem is replaced by the substantially weaker condition ‖Rm‖_n/2 C_S² ≤ ε_n.

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