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Nonlinear Analysis

Prescribing Gaussian and Geodesic curvature on surfaces with boundary

Andrea Malchiodi, Scuola Normale Superiore at Pisa and IAS

Location:  Hill 705
Date & time: Tuesday, 23 October 2018 at 1:40PM - 3:00PM

Abstract:  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 excluded.  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.

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