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 a singular Liouville equation under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n larger than 3 also in a supercritical regime. Finally, we state some open problems