A direct proof of Gromov's theorem

被引：0
|
作者：
Burago Y.D. [1 ]
Malev S.G. [2 ]
Novikov D.I. [2 ]
机构：
[1] St. Peterburg Department of the Steklov Mathematical Institute, St. Petersburg
[2] Department of Mathematics, Weizmann Institute of Science, Rehovot
来源：
Journal of Mathematical Sciences | 2009年 / 161卷 / 3期
关键词：
Russia; Local Mapping; Direct Proof; Hausdorff Distance; Mathematical Institute;
D O I：
10.1007/s10958-009-9559-z
中图分类号：
学科分类号：
摘要：
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. © 2009 Springer Science+Business Media, Inc.
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页码：361 / 367
页数：6
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