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

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Hausdorff Distance
Injectivity
Bibliographies
Sectional Curvature
Lipschitz
Exceed
Radius
Integer
Theorem
Bibliography

All Science Journal Classification (ASJC) codes

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

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
Burago, Yury D. ; Malev, S. G. ; Novikov, D. I. / A direct proof of Gromov's theorem. In: Journal of Mathematical Sciences. 2009 ; Vol. 161, No. 3. pp. 361-367.
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Burago, YD, Malev, SG & Novikov, DI 2009, 'A direct proof of Gromov's theorem', Journal of Mathematical Sciences, vol. 161, no. 3, pp. 361-367. https://doi.org/10.1007/s10958-009-9559-z

A direct proof of Gromov's theorem. / Burago, Yury D.; Malev, S. G.; Novikov, D. I.

In: Journal of Mathematical Sciences, Vol. 161, No. 3, 01.07.2009, p. 361-367.

Research output: Contribution to journalArticle

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