Regularity theory for 2-dimensional almost minimal currents II: branched center manifold

Camillo De Lellis, Emanuele Spadaro, and Luca Spolaor

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Submission date: 15. Sep. 2015
Pages: 74
published in: Annals of PDE, 3 (2017) 2, art-no. 18 
DOI number (of the published article): 10.1007/s40818-017-0035-7
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Abstract:
We construct a branched center manifold in a neighborhood of a singular point of a 2-dimensional integral current which is almost minimizing in a suitable sense. Our construction is the first half of an argument which shows the discreteness of the singular set for the following three classes of 2-dimensional currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-dimensional area minimizing cones.