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Extension of Lipschitz maps into 3-manifolds


Buyalo, S; Schroeder, V (2001). Extension of Lipschitz maps into 3-manifolds. Asian Journal of Mathematics, 5(4):685-704.

Abstract

We prove that the universal covering Y of a closed nonpositively curved 3-dimensional Riemannian manifold possesses the following Lipschitz extension property: there exists a constant c ≥ 1 such that every λ-Lipschitz map f : S → Y defined on s subset S of an arbitrary metric space X has a cλ-Lipschitz extension f¯ : X → Y.

Abstract

We prove that the universal covering Y of a closed nonpositively curved 3-dimensional Riemannian manifold possesses the following Lipschitz extension property: there exists a constant c ≥ 1 such that every λ-Lipschitz map f : S → Y defined on s subset S of an arbitrary metric space X has a cλ-Lipschitz extension f¯ : X → Y.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:06 Dec 2017 20:52
Publisher:International Press
ISSN:1093-6106
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.intlpress.com/AJM/p/2001/5_4/AJM-5-4-685-704.pdf
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1913816
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1020.53024
http://www.intlpress.com/AJM/AJM-v05.php#AJM-5-4 (Publisher)

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