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.

Uniqueness of tangent cones for two-dimensional almost-minimizing currents / DE LELLIS, Camillo; Spadaro, EMANUELE NUNZIO; Spolaor, Luca. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 70:7(2017), pp. 1402-1421. [10.1002/cpa.21690]

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

Camillo De Lellis;Emanuele Spadaro;
2017

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.
2017
two-dimensional minimal surfaces; regularity
01 Pubblicazione su rivista::01a Articolo in rivista
Uniqueness of tangent cones for two-dimensional almost-minimizing currents / DE LELLIS, Camillo; Spadaro, EMANUELE NUNZIO; Spolaor, Luca. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 70:7(2017), pp. 1402-1421. [10.1002/cpa.21690]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1117506
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