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Continuous Max-Flow Min-Cut Theorem for Currents on Riemannian Manifolds

A geometric-measure-theoretic analogue of the network max-flow/min-cut theorem on a compact Riemannian manifold: the maximum flux of a divergence-free unit-bounded vector field equals the minimum mass of a cut in a fixed relative homology class. Over the reals the minimal cut is a measured oriented minimal lamination rather than a hypersurface, and the choice of homology class encodes the domain's topology.

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THE MAX FLOW/MIN CUT THEOREM FOR CURRENTS AND LAMINATIONS AIDAN BACKUS Abstract. Motivated by

This paper proves a continuous analogue of the max-flow/min-cut theorem on a compact oriented Riemannian manifold with strictly mean-convex boundary, where flows are divergence-free vector fields of …