Calculus of Variations and Geometric Measure Theory

C. De Lellis - E. Spadaro - L. Spolaor

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

created by delellis on 21 Aug 2015
modified on 01 Dec 2020


Published Paper

Inserted: 21 aug 2015
Last Updated: 1 dec 2020

Journal: J. Differential Geom.
Volume: 116
Number: 1
Pages: 125-185
Year: 2020


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