Fine Structure of Singularities in Area-Minimizing Currents Mod(q)

2024/03/23 by Camillo De Lellis, De Lellis, Camillo, Paul Minter +3 · 1 citation
Computer Science · Mathematics · #35B65 #35J47 #49N60 #49Q05 #49Q15 #Analysis of PDEs (math.AP) #Coding theory and cryptography #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2403.15889

openalex publication_date 2024/03/23 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28

Abstract

We study fine structural properties related to the interior regularity of m-dimensional area minimizing currents mod(q) in arbitrary codimension. We show: (i) the set of points where at least one tangent cone is translation invariant along m-1 directions is locally a connected C^1,β submanifold, and moreover such points have unique tangent cones; (ii) the remaining part of the singular set is countably (m-2)-rectifiable, with a unique flat tangent cone (with multiplicity) at H^m-2-a.e. flat singular point. These results are consequences of fine excess decay theorems as well as almost monotonicity of a universal frequency function.

Cited by

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

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