English

Ricci Flow and Gromov Almost Flat Manifolds

Differential Geometry 2022-03-11 v1

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 diam2Kϵndiam^2 |K| \leq \epsilon_n in the Gromov--Ruh Theorem is replaced by the substantially weaker condition Rmn/2\|Rm\|_{n/2} CS2εn C_S^2 \leq \varepsilon_n.

Keywords

Cite

@article{arxiv.2203.05107,
  title  = {Ricci Flow and Gromov Almost Flat Manifolds},
  author = {Eric Chen and Guofang Wei and Rugang Ye},
  journal= {arXiv preprint arXiv:2203.05107},
  year   = {2022}
}
R2 v1 2026-06-24T10:08:06.536Z