Calculus of Variations and Geometric Measure Theory

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

Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation

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


Published Paper

Inserted: 21 aug 2015
Last Updated: 17 jul 2018

Journal: Transactions AMS
Volume: 370
Number: 3
Pages: 1783–1801
Year: 2018

To appear in Transactions of the AMS


We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of $2$-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of $3$-dimensional area minimizing cones.

Keywords: regularity, integral currents, area minimizing, semicalibrations