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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on quasi-isometries


Author: N. J. Kalton
Journal: Proc. Amer. Math. Soc. 131 (2003), 1225-1231
MSC (2000): Primary 46C05, 47H99
Published electronically: July 26, 2002
MathSciNet review: 1948114
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Abstract: We show that if $f:B_n\to\mathbb R^n$ is an $\epsilon-$quasi-isometry, with $\epsilon<1$, defined on the unit ball $B_n$ of $\mathbb R^n$, then there is an affine isometry $h:B_n\to\mathbb R^n$ with $\Vert f(x)-h(x)\Vert\le C\epsilon (1+\log n)$ where $C$ is a universal constant. This result is sharp.


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Additional Information

N. J. Kalton
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: nigel@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06663-7
PII: S 0002-9939(02)06663-7
Keywords: Quasi-isometries in Euclidean spaces
Received by editor(s): June 10, 2001
Received by editor(s) in revised form: November 27, 2001
Published electronically: July 26, 2002
Additional Notes: The author was supported by NSF grant DMS-9870027
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society