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A remark on quasi-isometries

Authors:	N J Kalton

Institution:	Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211

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 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 is a universal constant. This result is sharp.

Keywords:	Quasi-isometries in Euclidean spaces

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