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

Camillo De Lellis; Emanuele Spadaro; Luca Spolaor

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arXiv · 1508.05266

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

Camillo De Lellis·Emanuele Spadaro·Luca Spolaor

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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.

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Camillo De Lellis, Emanuele Spadaro, Luca Spolaor. 2015-08-21. Uniqueness of tangent cones for $2$-dimensional almost minimizing currents. https://arxiv.org/abs/1508.05266

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