Measure preserving maps with bounded total variation

Stefano Bianchini, Luca Talamini

Consider a piecewise affine Lipschitz map $\ddot{I}•:\hat{I}\text{c◯}\to \mathbb{R}$, where $\hat{I}\text{c◯}\subset {\mathbb{R}}^d$ is an open set, and assume that $x\mapsto x+t\nabla \ddot{I}•(x)$ is injective for almos…