Geodetically convex sets in the Heisenberg group ${\mathbb H}^n$

TL;DR

This paper classifies geodetically convex sets and functions within the Heisenberg group, providing a comprehensive understanding of their structure in this non-commutative geometric setting.

Contribution

It offers the first complete classification of geodetically convex sets and functions in the Heisenberg group, advancing the understanding of convexity in sub-Riemannian geometry.

Findings

Complete classification of geodetically convex sets in ${ m H}^n$

Characterization of geodetically convex functions in ${ m H}^n$

Insights into convexity properties in sub-Riemannian geometry

Abstract

We classify the geodetically convex sets and geodetically convex functions on the Heisenberg group ${\mathbb H}^n$, $n\geq 1$.