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Regularity of area minimizing currents I: Gradient L p estimates


De Lellis, Camillo; Spadaro, Emanuele (2014). Regularity of area minimizing currents I: Gradient L p estimates. Geometric and Functional Analysis, 24(6):1831-1884.

Abstract

In a series of papers, including the present one, we give a new, shorter proof of Almgren’s partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs. Our new a priori estimate is a higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays a key role in estimating the accuracy of the Lipschitz approximations.

Abstract

In a series of papers, including the present one, we give a new, shorter proof of Almgren’s partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs. Our new a priori estimate is a higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays a key role in estimating the accuracy of the Lipschitz approximations.

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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:December 2014
Deposited On:27 Jan 2015 16:33
Last Modified:08 Dec 2017 09:56
Publisher:Springer
ISSN:1016-443X
Additional Information:The final publication is available at Springer via http://dx.doi.org/10.1007/s00039-014-0306-3
Publisher DOI:https://doi.org/10.1007/s00039-014-0306-3

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