Optimal Lorentz estimates are established for Riesz potentials of L1 closed or co-closed forms on compact manifolds, implying bounds for the Hodge system with finite mass data.
Acta Math
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New proof that integer rectifiable currents with finite mass boundaries are integral, deduced from De Giorgi's BV theorem using cylindrical projections; also yields new compactness proof for integral currents.
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Potential Estimates and Hodge Systems with $L^1$ data on compact manifolds
Optimal Lorentz estimates are established for Riesz potentials of L1 closed or co-closed forms on compact manifolds, implying bounds for the Hodge system with finite mass data.
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Boundary rectifiability and compactness of integral currents via $BV$ functions
New proof that integer rectifiable currents with finite mass boundaries are integral, deduced from De Giorgi's BV theorem using cylindrical projections; also yields new compactness proof for integral currents.