The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with ${\int }_{M}Qd{V}_g=8{\pi }^2$

Abstract

In this paper we study the solutions of the $Q$-curvature equation on a 4-dimensional Riemannian manifold $(M,g)$ with ${\int }_{M}Qd{V}_g=8{\pi }^2$, proving some sufficient conditions for the existence.