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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 353, Pages 14–26
(Mi znsl1627)
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This article is cited in 1 scientific paper (total in 1 paper)
A direct proof of Gromov's theorem
Yu. D. Buragoa, S. G. Malevb, D. I. Novikovb a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Faculty of Mathematics and Computer Science, Weizmann Institute of Science
Abstract:
A new proof of a theorem by Gromov is given: for any $C>0$ and integer $n>1$, there exists a function
$\Delta_{C,n}(\delta)$ such that if the Gromov–Hausdorff distance between two complete Riemannian $n$-manifolds $V$ and $W$ is at most $\delta$, their sectional curvatures $|K_\sigma|$ do not exceed $C$, and their injectivity radii are at least $1/C$, then the Lipschitz distance between $V$ and $W$ is less than
$\Delta_{C,n}(\delta)$, and $\Delta_{C,n}(\delta)\to0$ as $\delta\to0$. Bibl. – 6 titles.
Received: 20.07.2007
Citation:
Yu. D. Burago, S. G. Malev, D. I. Novikov, “A direct proof of Gromov's theorem”, Geometry and topology. Part 10, Zap. Nauchn. Sem. POMI, 353, POMI, St. Petersburg, 2008, 14–26; J. Math. Sci. (N. Y.), 161:3 (2009), 361–367
Linking options:
https://www.mathnet.ru/eng/znsl1627 https://www.mathnet.ru/eng/znsl/v353/p14
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Abstract page: | 303 | Full-text PDF : | 104 | References: | 35 |
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