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Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation


De Lellis, Camillo; Spadaro, Emanuele; Spolaor, Luca (2018). Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation. Transactions of the American Mathematical Society, 370(3):1783-1801.

Abstract

We construct Lipschitz Q-valued functions which carefully approximate integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of 2-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-dimensional area minimizing cones.

Abstract

We construct Lipschitz Q-valued functions which carefully approximate integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of 2-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-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:2018
Deposited On:07 Mar 2018 16:33
Last Modified:14 Mar 2018 15:38
Publisher:American Mathematical Society
ISSN:0002-9947
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1090/tran/6995

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