Uniqueness of tangent cones for 2-dimensional almost minimizing currents

2015/08/21 by Camillo De Lellis, Emanuele Spadaro, De Lellis, Camillo +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35B65 #msc:35J47 #msc:49N60 #msc:49Q15

paper · pdf · doi:10.48550/arxiv.1508.05266

arxiv created 2015/08/21 · arxiv updated 2015/08/24

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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