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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
58/2015

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

Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

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.

Received:
15.09.15
Published:
15.09.15

Related publications

inJournal
2017 Repository Open Access
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor

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

In: Communications on pure and applied mathematics, 70 (2017) 7, pp. 1402-1421