Inserted: 21 aug 2015
Last Updated: 17 jul 2018
Journal: Ann. PDE
Pages: 85 pp
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: integral currents, area minimizing, semicalibrations, rergularity