| Abstract: |
| In this talk we outlines a general existence result regarding the prescription of curvatures on a disk under conformal changes of the metric. This problem is equivalent to solving a nonlinear partial differential equation with nonlinear Neumann boundary conditions. We addresses the case of negative Gaussian curvature. As a preliminary step, we focus on a symmetric setting.
Additionally, we present a non-existence result, demonstrating that the assumptions for existence are necessary.
This is a work in collaboration with Rafael Lopez Soriano and David Ruiz from the University of Granada. |
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