A PDE perspective on the flat chain conjecture

Andrea Marchese

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arXiv · 2511.06822

A PDE perspective on the flat chain conjecture

Andrea Marchese

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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.

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Andrea Marchese. 2025-11-10. A PDE perspective on the flat chain conjecture. https://arxiv.org/abs/2511.06822

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