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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