A model of anisotropic branched optimal transport

TL;DR

This paper introduces a novel anisotropic optimal transport model utilizing currents, establishing existence of minimizers in planar cases and under hypermetric conditions in higher dimensions.

Contribution

It develops a new anisotropic optimal transport framework based on currents, with existence results for minimizers in various dimensions.

Findings

Existence of minimizers in planar anisotropic transport problems.

Minimizer existence in higher dimensions under hypermetric conditions.

The model separates cost factors into directional and multiplicity components.

Abstract

We propose a new anisotropic optimal transport model based on the theory of currents, where the anisotropic cost function splits as the product of a factor depending only on the spatial direction and a factor depending only on the multiplicity of the current. We prove that the planar transport problem admits a minimizer. In arbitrary dimension, we show that a minimizer exists provided that the ambient space endowed with the anisotropic norm is hypermetric.