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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 (www.arxiv.org) 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
59/2015

Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation

Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Abstract

We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of $2$-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of $3$-dimensional area minimizing cones.

Received:
Sep 15, 2015
Published:
Sep 15, 2015

Related publications

inJournal
2018 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Regularity theory for \(2\)-dimensional almost minimal currents I : Lipschitz approximation

In: Transactions of the American Mathematical Society, 370 (2018) 3, pp. 1783-1801