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Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor
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.