TY - JOUR

T1 - A direct proof of Gromov's theorem

AU - Burago, Yu D.

AU - Malev, S. G.

AU - Novikov, D. I.

PY - 2009/7

Y1 - 2009/7

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=70449526799&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9559-z

DO - 10.1007/s10958-009-9559-z

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AN - SCOPUS:70449526799

SN - 1072-3374

VL - 161

SP - 361

EP - 367

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 3

ER -