# Regularity theory for $2$-dimensional almost minimal currents III: blowup

created by delellis on 21 Aug 2015
modified by spolaor on 05 Oct 2017

[BibTeX]

Accepted Paper

Inserted: 21 aug 2015
Last Updated: 5 oct 2017

Journal: JDG
Year: 2017

Abstract:

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.