Existence of complete conformal metrics on ${\mathbb{R}}^n$ with prescribed Q-curvature

Mingxiang Li, Biao Ma

Given a smooth function $f(x)$ on ${\mathbb{R}}^n$ which is positive somewhere and satisfies $f(x)=O(|x{|}^{-l})$ for any $l>\frac{n}{2}$, we show that there exists a complete and conf…