On the fundamental regularity theorem for mass-minimizing flat chains

2024/08/07 by White, Brian · 1 citation
#49Q15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.04083

Abstract

In the theory of flat chains with coefficients in a normed abelian group, we give a simple necessary and sufficient condition on a group element g in order for the following fundamental regularity principle to hold: if a mass-minimizing chain is, in a ball disjoint from the boundary, sufficiently weakly close to a multiplicity g disk, then, in a smaller ball, it is a C^1,α perturbation with multiplicity g of that disk.

Cited by

• The Hasse Principle for Geometric Variational Problems: An Illustration via Area-minimizing Submanifolds

Related

• On the structure of flat chains with finite mass
• An inequality on the mass of image of rectifiable chain under chain map
• Regularity dimensions: quantifying doubling and uniform perfectness
• Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds
• A PDE perspective on the flat chain conjecture