A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing

TL;DR

This paper demonstrates that a specific family of entire intrinsic minimal graphs in the Heisenberg group do not minimize perimeter, challenging assumptions about minimality in sub-Riemannian geometry.

Contribution

It identifies a family of entire intrinsic minimal graphs in the Heisenberg group that are not perimeter minimizing, providing new insights into minimal surface theory.

Findings

Certain entire intrinsic minimal graphs are not perimeter minimizing

Challenges previous assumptions about minimality in the Heisenberg group

Contributes to understanding of sub-Riemannian minimal surfaces

Abstract

We prove that a family of entire intrinsic minimal graphs in the Heisenberg group are not perimeter minimizing.