An integral formula for the $Q$-prime curvature in 3-dimensional CR geometry

TL;DR

This paper derives an integral formula for the total $Q'$-curvature in three-dimensional CR geometry, linking Green's functions of the CR Laplacian and $P'$-operator, under specific positivity conditions.

Contribution

It introduces a novel integral formula for total $Q'$-curvature in 3D CR manifolds, connecting Green's functions of key differential operators.

Findings

Established an integral formula for total $Q'$-curvature.

Linked Green's functions of CR Laplacian and $P'$-operator.

Applicable to CR manifolds with positive Yamabe constant and nonnegative Paneitz operator.

Abstract

We give an integral formula for the total $Q^\prime$-curvature of a three-dimensional CR manifold with positive CR Yamabe constant and nonnegative Paneitz operator. Our derivation includes a relationship between the Green's functions of the CR Laplacian and the $P^\prime$-operator.