### Abstract

A new proof of a theorem by Gromov is given: for any positive C and any integer n greater than 1, there exists a function Δ_{C,n}(δ) such that if the Gromov-Hausdorff distance between two complete Riemannian n-manifolds V and W is at most δ, their sectional curvatures K_{σ} do not exceed C, and their injectivity radii are at least 1/C, then the Lipschitz distance between V and W is less than Δ_{C,n}(δ), and Δ_{C,n}(δ) → 0 as δ → 0. Bibliography: 6 titles.

Original language | English (US) |
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Pages (from-to) | 361-367 |

Number of pages | 7 |

Journal | Journal of Mathematical Sciences |

Volume | 161 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2009 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Applied Mathematics

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## Cite this

Burago, Y. D., Malev, S. G., & Novikov, D. I. (2009). A direct proof of Gromov's theorem.

*Journal of Mathematical Sciences*,*161*(3), 361-367. https://doi.org/10.1007/s10958-009-9559-z