Equilateral dimension of the Heisenberg group

TL;DR

This paper determines that the maximum size of an equilateral set in the first Heisenberg group with the Korányi metric is four, providing a precise geometric characterization.

Contribution

The paper establishes that the equilateral dimension of the first Heisenberg group with the Korányi metric is exactly four, a new result in geometric analysis of sub-Riemannian spaces.

Findings

Equilateral dimension of the Heisenberg group is 4.

Provides geometric insights into the structure of the Heisenberg group.

Advances understanding of metric properties in sub-Riemannian geometry.

Abstract

Let $\mathfrak{H}$ be the first Heisenberg group equipped with the Kor\'anyi metric $d$. We prove that the equilateral dimension of $\mathfrak{H}$ is 4.