A direct proof of Gromov's theorem

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

doi:10.1007/s10958-009-9559-z

A direct proof of Gromov's theorem

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	361-367
Number of pages	7
Journal	Journal of Mathematical Sciences (Switzerland)
Volume	161
Issue number	3
DOIs	https://doi.org/10.1007/s10958-009-9559-z
State	Published - Jul 2009

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-009-9559-z

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AB - 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.

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A direct proof of Gromov's theorem

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