Prescribing Gaussian and Geodesic curvature on surfaces with boundary

Andrea Malchiodi, SISSA
Fine Hall 314

We consider the classical problem of finding conformal metrics on a
surface such that both the Gaussian and the geodesic curvatures are
assigned functions.
We use variational methods and blow-up analysis to find existence of
solutions under suitable assumptions. A peculiar aspect of the problem
is that there are blow-up profiles with infinite volume that have to be 
In order to do this, we classify their stability properties and employ
holomorphic vector fields. This is joint work with R. Lopez-Soriano and D. Ruiz.