A note on the Slicing of $(k+1)$-Currents in the Heisenberg Group $\mathbb{H}^n$ in the case $k=n$

TL;DR

This paper discusses the open problem of slicing $(k+1)$-currents in the Heisenberg group specifically for the case when $k=n$, aiming to advance understanding in geometric measure theory.

Contribution

It addresses the unresolved case $k=n$ in the slicing of currents within the Heisenberg group, providing insights and potential pathways for future solutions.

Findings

Clarifies the open case $k=n$ in current slicing theory

Provides new perspectives on geometric measure theory in Heisenberg groups

Encourages further research into the unresolved problem

Abstract

This paper aims to expand on the open case $k=n$ regarding Proposition 3.6[1] and hopefully foster curiosity for its resolution.