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

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.

References in corpus (2)

• Uniqueness of Tangent Cones to Positive-(p,p) Integral Cycles
• Semi-calibrated 2-currents are pseudo holomorphic, with applications

Cited by in corpus (1)

• On the number of singular points for planar multivalued harmonic functions