Proceedings of the American Mathematical Society

Author(s): N. J. Kalton
Journal: Proc. Amer. Math. Soc. 131 (2003), 1225-1231.
MSC (2000): Primary 46C05, 47H99
Posted: July 26, 2002
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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

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.

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