Higher integrability and approximation of minimal currents

2009/10/30 by Camillo De Lellis, Emanuele Spadaro, De Lellis, Camillo +2 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.0910.5878

This paper has been withdrawn by the authors, because an extended new version (where the results are proven in general Riemannian manifolds) has been posted: cf. article 1306.1195

openalex publication_date 2009/10/30 · arxiv created 2013/06/07 · arxiv updated 2013/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new, simpler proof of the main approximation theorem for area minimizing current contained in Almgren's Big regularity paper. Our proof relies on a new estimate concerning the higher integrability of the quantity called here the excess density, which in turn we link to an analogous property of harmonic multiple valued functions.

Cited by

• Regularity of area minimizing currents I: gradient L^p estimates

Related

• Regularity of higher codimension area minimizing integral currents
• Regularity of area minimizing currents I: gradient L^p estimates
• Lipschitz approximation for general almost area minimizing currents
• Regularity of area minimizing currents III: blow-up
• The size of the singular set of area-minimizing currents