A direct proof of Gromov's theorem

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

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)361-367
Number of pages7
JournalJournal of Mathematical Sciences
Issue number3
StatePublished - Jul 2009
Externally publishedYes


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