Measure preserving maps with bounded total variation

Stefano Bianchini, Luca Talamini

Consider a piecewise affine Lipschitz map $\varphi :\Omega \to \mathbb{R}$, where $\Omega \subset {\mathbb{R}}^d$ is an open set, and assume that $x\mapsto x+t\nabla \varphi (x)$ is injective for almost ev…