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

2015/08/22 by Camillo De Lellis, Emanuele Spadaro, De Lellis, Camillo +3 · 1 citation
Computer Science · Mathematics · #35B65 #35J47 #49N60 #49Q15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Approximation and Integration #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1508.05507

openalex publication_date 2015/08/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We construct Lipschitz Q-valued functions which approximate carefully\nintegral currents when their cylindrical excess is small and they are almost\nminimizing in a suitable sense. This result is used in two subsequent works to\nprove the discreteness of the singular set for the following three classes of\n2-dimensional integral currents: area minimizing in Riemannian manifolds,\nsemicalibrated and spherical cross sections of 3-dimensional area minimizing\ncones.\n

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• Structure of two-dimensional mod(q) area-minimizing currents near flat singularities: the codimension one case

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