A remark on quasi-isometries

Kalton, N.

doi:10.1090/S0002-9939-02-06663-7

A remark on quasi-isometries
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by N. J. Kalton PDF

Proc. Amer. Math. Soc. 131 (2003), 1225-1231 Request permission

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 $\|f(x)-h(x)\|\le C\epsilon (1+\log n)$ where $C$ is a universal constant. This result is sharp.

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