Prescribing the Gaussian curvature on a compact surface and the geodesic curvature on its boundary
speaker: David Ruiz (Universidad de Granada)abstract: The problem of prescribing the Gaussian curvature on compact surfaces via a conformal change of the metric dates back to the works of Berger, Moser, Kazdan & Warner, etc. Our aim is to consider surfaces with boundary where we also prescribe the geodesic curvature of the border. This gives rise to a Liouville equation under nonlinear Neumann boundary conditions.
In this talk we address the case of negative Gaussian curvature, and we will focus on the blow-up analysis of the solutions. Here the cancellation between the area and length terms make it possible to have blowing-up solutions with unbounded total mass. This phenomenon seems to be entirely new in the related literature. We are able to give a complete description of this question under Morse index restrictions.
This is joint work with Andrea Malchiodi (SNS Pisa) and Rafael López Soriano (U. Valencia).
timetable:
Thu 28 Nov, 11:30 - 12:20, Aula Dini
documents:
talk
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