A variational approach to singular Liouville equations

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Date(s) - 21 février 2012

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We consider a class of Liouville equations on compact surfaces, motivated by the problem of prescribing conformal metrics with conical singularities, as well as by physical models in abelian Chern-Simons and Electroweak theory. We describe some new scaling invariant improvements of the Moser-Trudinger inequality, which yield existence of solutions once combined with topological arguments.