BIRS Workshop Lecture Videos
The space of one-phase free boundary solutions in the plane Kamburov, Nikola
In joint work with David Jerison we study the compactness of the space of solutions to the one-phase free boundary problem in the disk, whose positive phase is of fixed genus. We describe the local structure of the free boundary and obtain rigidity estimates on its shape. Via a correspondence due to Traizet, our results are direct counterparts to theorems by Colding and Minicozzi for minimal surfaces.
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