Higher integrability and approximation of minimal currents

Abstract

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.

This paper has been withdrawn by the authors, because an extended new version (where the results are proven in general Riemannian manifolds) has been posted: cf. article 1306.1195

References in corpus (1)

• Q-valued functions revisited

Cited by in corpus (4)

• Q-valued functions revisited
• Lower semicontinuous functionals for Almgren's multiple valued functions
• Semi-calibrated 2-currents are pseudo holomorphic, with applications
• Complex varieties and higher integrability of Dir-minimizing Q-valued functions