On the existence of $L^p$-Optimal Transport maps for norms on ${\mathbb{R}}^N$

Guoxi Liu, Mattia Magnabosco, Yicheng Xia

In this paper, we prove existence of $L^p$-optimal transport maps with $p\in (1,\infty )$ in a class of branching metric spaces defined on ${\mathbb{R}}^N$. In particular, we introdu…