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

Camillo De Lellis, Emanuele Spadaro, and Luca Spolaor

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Submission date: 15. Sep. 2015
Pages: 27
published in: Transactions of the American Mathematical Society, 370 (2018) 3, p. 1783-1801 
DOI number (of the published article): 10.1090/tran/6995
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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.