Regularity of area minimizing currents mod p

• Published in: Geometric and functional analysis Vol. 30; no. 5; pp. 1224 - 1336
• Main Authors: De Lellis, Camillo, Hirsch, Jonas, Marchese, Andrea, Stuvard, Salvatore
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2020
• Subjects: Analysis; Mathematics; Mathematics and Statistics; Area minimizing currents; Minimal surfaces; Center manifold; 49N60; 49Q05; 49Q15; Regularity theory; 35B65; Multiple valued functions; Blow-up analysis; 35J47

We establish a first general partial regularity theorem for area minimizing currents mod ( p ) , for every p , in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m -dimensional area minimizing current mod ( p ) cannot be larger...