Transport and Interface: an Uncertainty Principle for the Wasserstein distance

Amir Sagiv, Stefan Steinerberger

Let $f:[0,1{]}^d\to \mathbb{R}$ be a continuous function with zero mean and interpret $f_{+}=\max (f,0)$ and $f_{-}=-\min (f,0)$ as the densities of two measures. We pr…