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.

引用

页码：361 / 367

页数：6

共 6 条

[1] Burago D.Y., Burago Y.D., Ivanov S.V., A Course in Metric Geometry, Amer. Math. Soc., 33, (2001)
[2] Burago Y.D., Zalgaller V.A., Introduction to Riemannian Geometry, (1994)
[3] Chavel I., Riemannian Geometry - a Modern Introduction, 108, (1993)
[4] Gromov M., Metric Structures for Riemannian and Non-Riemannian Spaces, (1999)
[5] Jost J., Riemannian Geometry and Geometric Analysis, (2002)
[6] Karcher H., Riemannian center of mass and mollifier smoothing, Comm. Pure Appl. Math., 30, pp. 509-541, (1977)

← 1 →