@article {2011, title = {A class of existence results for the singular Liouville equation}, journal = {Comptes Rendus Mathematique 349 (2011) 161-166}, year = {2011}, publisher = {Elsevier}, abstract = {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{\textendash}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.}, doi = {10.1016/j.crma.2010.12.016}, url = {http://hdl.handle.net/1963/5793}, author = {Alessandro Carlotto and Andrea Malchiodi} }