Uniqueness of tangent cones for 2-dimensional almost minimizing currents

Camillo De Lellis, Emanuele Spadaro, and Luca Spolaor

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Submission date: 15. Sep. 2015
Pages: 19
published in: Communications on pure and applied mathematics, 70 (2017) 7, p. 1402-1421 
DOI number (of the published article): 10.1002/cpa.21690
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Abstract:
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.