Regularity Theory for 2-Dimensional Almost Minimal Currents II: Branched Center Manifold
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Author(s)
De Lellis, Camillo
Spadaro, Emanuele
Spolaor, Luca
Date Issued
October 2017
Journal
Annals of PDE
Publisher
Springer International Publishing
Citation
De Lellis, Camillo, et al. “Regularity Theory for 2-Dimensional Almost Minimal Currents II: Branched Center Manifold.” Annals of PDE, vol. 3, no. 2, Dec. 2017.
Version
Author's final manuscript
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. Keywords: Area-minimizing currents, Regularity, Two-dimensional, Branching singularities, Center manifold
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s40818-017-0035-7
