Calculus of Variations and Geometric Measure Theory

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

Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold

created by delellis on 21 Aug 2015
modified on 17 Jul 2018


Published Paper

Inserted: 21 aug 2015
Last Updated: 17 jul 2018

Journal: Ann. PDE
Volume: 2
Number: 18
Pages: 85 pp
Year: 2017


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