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MiS Preprint

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

Camillo De Lellis, Emanuele Spadaro and Luca Spolaor


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.


Related publications

2017 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

Uniqueness of tangent cones for two-dimensional almost-minimizing currents

In: Communications on pure and applied mathematics, 70 (2017) 7, pp. 1402-1421