New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces (Q659922)

From the abstract: We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self-dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.