Factorization and piecewise affine approximation of bi-Lipschitz
mappings on large sets
Factorization and piecewise affine approximation of bi-Lipschitz
mappings on large sets
A well-known open problem asks whether every bi-Lipschitz homeomorphism of $\mathbb{R}^d$ factors as a composition of mappings of small distortion. We show that every bi-Lipschitz embedding of the unit cube $[0,1]^d$ into $\mathbb{R}^d$ factors into finitely many global bi-Lipschitz mappings of small distortion, outside of an exceptional set of arbitrarily …