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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.
