A Survey On Non Characteristic Heisenberg Group Domains

TL;DR

This survey explores non characteristic domains in Heisenberg groups, proving certain geometric conditions for such domains and proposing a conjecture about their classification.

Contribution

It provides a classification of non characteristic domains in Heisenberg groups and introduces a conjecture for their complete characterization.

Findings

Bounded domains diffeomorphic to a solid torus are non characteristic.

Proved that the center of the group as rotation axis implies non characteristic property.

Proposed a conjecture relating non characteristic domains to solid tori in Heisenberg groups.

Abstract

In this work, we give a survey on non characteristic domains of Heisenberg groups. We prove that bounded domains which are diffeomorphic to the solid torus having the center of the group as rotation axis, are non characteristic. Then, we state the following conjecture : The bounded non characteristic domains of the Heisenberg group of dimension 1 are those diffeomorphic to a solid torus having the center of the group as rotation axis.