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 -