The max flow/min cut theorem for currents and laminations

TL;DR

This paper develops a continuous analogue of the max flow/min cut theorem that incorporates the topology of the domain, motivated by applications in holography and Teichmüller theory.

Contribution

It introduces a novel continuous version of the max flow/min cut theorem that considers topological features, extending classical discrete results.

Findings

Established a continuous max flow/min cut duality with topological considerations

Extended classical theorem to domains with complex topology

Provided mathematical tools applicable to holography and Teichmüller theory

Abstract

Motivated by applications to holography and Teichm\"uller theory, we prove a continuous analogue of the max flow/min cut theorem which also takes the topology of the domain into account.