New Improved Moser-Trudinger Inequalities and Singular Liouville Equations on Compact Surfaces

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. © 2011 Springer Basel AG.