TitleRegularity of area-minimizing currents I: L^p gradient estimates
Publication TypeJournal Article
Year of Publication2014
AuthorsDe Lellis C., Spadaro E.
JournalGeometric and Functional Analysis
Volume24
Pagination1831–1884
Date PublishedDecember
PublisherSpringer
Type of ArticleInterior regularity
ISSN1016-443X
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.

Notes

Geom. Funct. Anal. 24 (2014), no. 6, 1831–1884.

URLhttps://link.springer.com/article/10.1007/s00039-014-0306-3
DOI10.1007/s00039-014-0306-3
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