Calculus of Variations and Geometric Measure Theory

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

Uniqueness of tangent cones for $2$-dimensional almost minimizing currents

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


Published Paper

Inserted: 21 aug 2015
Last Updated: 17 jul 2018

Journal: Comm. Pure Appl. Math.
Volume: 70
Number: 7
Pages: 1402–1421
Year: 2017


We consider $2$-dimensional integer rectifiable currents which are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area minimizing currents in the euclidean space. This note is also the first step in a regularity program for semicalibrated $2$-dimensional currents and spherical cross sections of $3$-dimensional area minimizing cones.

Keywords: regularity, Area minimizing currents, tangent cones