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math.AP2025
A PDE perspective on the flat chain conjecture
Andrea Marchese
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.…
math.AP2024
A refined Lusin type theorem for gradients
Luigi De Masi, Andrea Marchese
We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field coincides with the gradient of a function $g…