Higher integrability and approximation of minimal currents

Mathematics – Analysis of PDEs

Scientific paper

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40 pages

Scientific paper

We give a new, simpler proof of the main approximation theorem for area
minimizing current contained in Almgren's Big regularity paper. Our proof
relies on a new estimate concerning the higher integrability of the quantity
called here the excess density, which in turn we link to an analogous property
of harmonic multiple valued functions.

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