Local and nonlocal singular Liouville equations in Euclidean spaces

We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation −Deltaw = e^(nw) − c δ_0 on R^n, under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n ≥ 3 also in a supercritical regime. Finally, we state some open problems