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MiS Preprint
55/2013

Regularity of area minimizing currents I: gradient $L^p$ estimates

Camillo De Lellis and Emanuele Spadaro

Abstract

In a series of papers, including the present one, we give a new, shorter proof of Almgren's partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement in the regularity assumption for the latter.

This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs.

Our new a priori estimate is an higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays a key role in estimating the accuracy of the Lipschitz approximations.

Received:
Jun 5, 2013
Published:
Jun 17, 2013

Related publications

inJournal
2014 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Regularity of area minimizing currents I : gradient Lp estimates

In: Geometric and functional analysis, 24 (2014) 6, pp. 1831-1884