Prescription of Q-curvature on closed Riemannian manifolds

TL;DR

This paper proves that on certain closed Riemannian manifolds, any smooth positive function can be realized as the Q-curvature of some metric, extending the understanding of curvature prescription problems.

Contribution

It establishes the existence of metrics with prescribed Q-curvature on closed manifolds with positive Paneitz invariant, for dimensions greater than four.

Findings

Existence of metrics with prescribed Q-curvature for given positive functions.

Extension of curvature prescription results to higher dimensions.

Application of Paneitz operator in curvature prescription problem.

Abstract

In this paper it is hown that given any smooth, positive function f on a closed, smooth manifold of dimension greater than four and with positive Paneitz invariant, there exists a metric on M such that $Q_g$ = f.