Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents
Camillo De Lellis, Emanuele Spadaro, Luca Spolaor · Communications on Pure and Applied Mathematics · 2017
Abstract We consider two‐dimensional integer rectifiable currents that 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 two‐dimensional currents and spherical cross sections of three‐dimensional area‐minimizing cones.© 2017 Wiley Periodicals, Inc.