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

De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca

doi:10.1090/tran/6995

Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation
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by Camillo De Lellis, Emanuele Spadaro and Luca Spolaor PDF

Trans. Amer. Math. Soc. 370 (2018), 1783-1801 Request permission

Abstract:

We construct Lipschitz $Q$-valued functions which carefully approximate 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.

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