PDE Seminar Abstracts

An existence result for singular Liouville equations on compact surfaces

David Ruiz
University of Granada, Spain
13 Dec 2010, 3-4pm, Carslaw Room 350


In this talk we will consider a Liouville equation on a compact surface. This problem appears in physical models like the abelian Chern-Simons-Higgs theory and the Electroweak theory. Moreover, it is also related to the problem of prescribing the Gaussian curvature of a surface via a conformal deformation of the metric. If the surface has some conical points, Dirac deltas appear in the equation; this is the case we are interested in.

Our techniques are variational, that is, we look for solutions as critical points of an associated energy functional. In order to do that, the study of the topology of the sublevels of that functional becomes very important. This is accomplished thanks to a convenient Moser-Trudinger type inequality.