Inserted: 21 aug 2015
Last Updated: 1 dec 2020
Journal: J. Differential Geom.
We analyze the asymptotic behavior of a $2$-dimensional integral current which is almost minimizing in a suitable sense at a singular point. Our analysis is the second 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: regularity, integral currents, area minimizing, semicalibrations