%0 Journal Article %J Comptes Rendus Mathematique 349 (2011) 161-166 %D 2011 %T A class of existence results for the singular Liouville equation %A Alessandro Carlotto %A Andrea Malchiodi %X We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. %B Comptes Rendus Mathematique 349 (2011) 161-166 %I Elsevier %G en %U http://hdl.handle.net/1963/5793 %1 5648 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-07T07:37:16Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2010.12.016