Regularity of area minimizing currents I: gradient Lp estimates
Camillo De Lellis and Emanuele Spadaro
Contact the author: Please use for correspondence this email.
Submission date: 05. Jun. 2013
published in: Geometric and functional analysis, 24 (2014) 6, p. 1831-1884
DOI number (of the published article): 10.1007/s00039-014-0306-3
Download full preprint: PDF (593 kB)
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 in 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 an 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.