Title: Factorization and piecewise affine approximation of bi-Lipschitz maps on large sets
Speaker: Guy C. David, Ball State University
Abstract:
A well-known open problem asks whether every bi-Lipschitz homeomorphism of Euclidean space factors as a composition of mappings of small distortion. Restricting our domain to the unit d-cube, we will describe recent work proving that a quantitative version of this factorization holds outside of an exceptional set of arbitrarily small Lebesgue measure (which in this setting cannot always be removed). We will also discuss connections with the problem of approximating homeomorphisms by piecewise affine homeomorphisms. The new results are joint with Matthew Romney and Raanan Schul.