A continuous model of transportation in the Heisenberg group

TL;DR

This paper introduces a continuous transportation model within the Heisenberg group, analyzing its dual form and connections to optimal transport problems for various p-values, including the limit case p=1.

Contribution

It develops a novel minimization framework with divergence constraints in the Heisenberg group and explores its relation to classical optimal transport problems.

Findings

Established dual formulation of the model.

Linked the model to congested optimal transport for p>1.

Analyzed the limit case p=1 and its relation to Monge-Kantorovich problem.

Abstract

We present a minimization problem with a horizontal divergence-type constraint in the Heisenberg group. Our study explores its dual formulation and examines its relationship with the congested optimal transport problem, for $1 < p < +\infty$, as well as the Monge-Kantorovich problem, in the limite case $p=1$.