Leaf superposition property for integer rectifiable currents

TL;DR

This paper proves that certain positive, boundary-less integer rectifiable currents can be represented as a superposition of finitely many BV graph functions, providing a new structural insight.

Contribution

It introduces a novel superposition property for a class of integer rectifiable currents, linking them to finitely many BV functions.

Findings

Currents can be expressed as superpositions of BV graph functions

Establishes a structural decomposition for positive boundary-less currents

Provides a new perspective on the geometry of rectifiable currents

Abstract

We consider the class of integer rectifiable currents without boundary satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.