Bi-Lipschitz concordance implies bi-Lipschitz isotopy

We modify the proof of an earlier result of ours to deforming topological, bi-Lipschitz, and quasiconformal embeddings of an open subsetU ofR ⁿ which now are of small uniform distance from the inclusion map. As an application we show that two bi-Lipschitz homeomorphismsf ₀,f ₁:R ⁿRⁿ are bi-Lipschitz isotopic if and only ifd(f ₀,f ₁)<.Research supported in part by a grant from the Institut Mittag-Leffler.