A PDE perspective on the flat chain conjecture

Abstract

This survey summarizes recent progress on the flat chain conjecture, which asserts the equivalence between metric currents and flat chains with finite mass in the Euclidean space. In particular, we focus on recent work showing that the conjecture is equivalent to a Lipschitz regularity estimate for a certain PDE.

Survey for the proceedings of the conference "Winter School in Geometric Measure Theory", Hangzhou, January 2025