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