Densities non-realizable as the Jacobian of a 2-dimensional bi-Lipschitz map are generic

摘要

In this work, positive functions defined on the plane are considered from a generic viewpoint, both in the continuous and bounded setting. By pursuing on constructions of Burago-Kleiner and McMullen, we show that, generically, such a function cannot be written as the Jacobian of a bi-Lipschitz homeomorphism.