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Uniqueness of tangent cones for two-dimensional almost-minimizing currents


De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca (2017). Uniqueness of tangent cones for two-dimensional almost-minimizing currents. Communications on Pure and Applied Mathematics, 70(7):1402-1421.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1 July 2017
Deposited On:18 Jan 2018 11:15
Last Modified:19 Mar 2018 08:58
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0010-3640
Additional Information:This is the peer reviewed version of the following article: Communications on Pure and Applied Mathematics, Volume 70, Issue 7, July 2017, Pages 1402–1421 , which has been published in final form at https://doi.org/10.1002/cpa.21690. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms).
OA Status:Green
Publisher DOI:https://doi.org/10.1002/cpa.21690

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