Calculus of Variations and Geometric Measure Theory
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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 24 May 2017


Accepted Paper

Inserted: 21 aug 2015
Last Updated: 24 may 2017

Journal: Comm. Pure Appl. Math.
Year: 2015


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


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