MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Camillo De Lellis and Emanuele Spadaro


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.


Related publications

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