A Variational approach to Liouville equations

A Variational approach to Liouville equations

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Andrea Malchiodi , PISA
Fine Hall 314

Liouville equations arise when trying to uniformize curvatures or to extremise energies depending on spectra of surfaces. We consider cases when Gauss-Bonnet integrals are "large", as it might happen in presence of conical singularities. We prove existence of solutions combining geometric functional inequalities and a micro/macroscopic study of conformal volume distribution.