00981nas a2200121 4500008004100000245006900041210006700110260001300177520058600190100002500776700002200801856003600823 2011 en d00aA class of existence results for the singular Liouville equation0 aclass of existence results for the singular Liouville equation bElsevier3 aWe 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 Chernâ€“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.1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/5793