CR Yamabe constant, CR Yamabe flow and its soliton

TL;DR

This paper investigates the CR Yamabe constant on infinite coverings, establishes a uniqueness theorem for the CR Yamabe flow on complete noncompact manifolds, and explores properties of CR Yamabe solitons in such settings.

Contribution

It introduces new results on the CR Yamabe constant, proves a uniqueness theorem for the flow, and analyzes properties of solitons on noncompact CR manifolds.

Findings

CR Yamabe constant studied on infinite conformal coverings.

Uniqueness theorem established for the CR Yamabe flow.

Properties of CR Yamabe solitons on noncompact manifolds derived.

Abstract

On a compact strictly pseudoconvex CR manifold $(M,\th)$, we consider the CR Yamabe constant of its infinite conformal covering. By using the maximum principles, we then prove a uniqueness theorem for the CR Yamabe flow on a complete noncompact CR manifold. Finally we obtain some properties of the CR Yamabe soliton on complete noncompact CR manifolds.