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Rough initial data

Wednesday 14th December 2005 - 11:30 to 12:30
INI Seminar Room 1

The story of constant mean curvature $H^s$ solutions of the constraint equations with $s>3/2$ has largely been completed, both for asymptotically Euclidean and compact manifolds. It turns out that the standard existence results for smooth solutions extend fully and naturally to the low regularity setting. In this talk I will describe how these results were obtained. One point of interest, even for smooth solutions, is that the rough theory leads to a unified and simpler approach for working with the various cases of the CMC conformal method on compact manifolds.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons