Uniqueness of Tangent Cones for Two‐Dimensional Almost‐Minimizing Currents. Issue 7 (1st March 2017)

• Record Type: Journal Article
• Authors: De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca
• Is Part Of: Communications on pure and applied mathematics. Volume 70:Issue 7(2017:Jul.)
• Page Start: 1402
• Page End: 1421
• Publication Date: 2017-03-01
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21690
• Languages: English
• ISSNs: 0010-3640

Abstract

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.