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arXiv · 1508.05509

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

Camillo De Lellis·Emanuele Spadaro·Luca Spolaor
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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.

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Camillo De Lellis, Emanuele Spadaro, Luca Spolaor. 2017-09-04. Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold. https://arxiv.org/abs/1508.05509

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