A direct proof of Gromov's theorem

Yury D. Burago, S. G. Malev, D. I. Novikov

Research output: Contribution to journalArticle

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 ΔC,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 Kσ do not exceed C, and their injectivity radii are at least 1/C, then the Lipschitz distance between V and W is less than ΔC,n(δ), and ΔC,n(δ) → 0 as δ → 0. Bibliography: 6 titles.

Original languageEnglish (US)
Pages (from-to)361-367
Number of pages7
JournalJournal of Mathematical Sciences
Volume161
Issue number3
DOIs
StatePublished - Jul 1 2009

All Science Journal Classification (ASJC) codes

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

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    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