$\bar{Q}'$-curvature flow on Pseudo-Einstein CR manifolds

TL;DR

This paper investigates a geometric flow on three-dimensional Pseudo-Einstein CR manifolds aimed at prescribing the $ar{Q}'$-curvature, demonstrating convergence under certain conditions.

Contribution

It introduces a gradient flow approach for prescribing $ar{Q}'$-curvature and proves its convergence on Pseudo-Einstein CR manifolds.

Findings

Flow converges to a solution under suitable assumptions

Provides a method for prescribing $ar{Q}'$-curvature

Advances understanding of geometric flows on CR manifolds

Abstract

In this paper we consider the problem of prescribing the $\bar{Q}'$-curvature on three dimensional Pseudo-Einstein CR manifolds. We study the gradient flow generated by the related functional and we will prove its convergence to a limit function under suitable assumptions.