A maximum principle for pointwise energies of quadratic Wasserstein minimal networks

TL;DR

This paper establishes a maximum principle for convex energy functionals on quadratic Wasserstein spaces, revealing new structural insights into minimal networks in optimal transport theory.

Contribution

It introduces a maximum principle applicable to minimal networks in quadratic Wasserstein spaces, advancing understanding of their structure and properties.

Findings

Maximum principle holds for convex energies on minimal networks

Structural properties of minimal networks are derived from the maximum principle

Implications for optimal transport and network design are discussed

Abstract

We show that suitable convex energy functionals on a quadratic Wasserstein space satisfy a maximum principle on minimal networks. We explore consequences of this maximum principle for the structure of minimal networks.