DIFFERENTIAL GEOMETRY/PDE SEMINAR

Thursday, May 1, 2003 Padelford C-36 2:30 pm (Note: Special Day and Time!)

Some applications of the Corvino-Schoen method for solving the constraint equations

Piotr T. Chrusciel (Université de Tours, France)

I will present recent work with Erwann Delay, in which we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces using the Corvino-Schoen technique. As a corollary we prove existence of initial data for many black holes which are exactly Kerr - or exactly Schwarzschild - both near infinity and near each of the connected components of the apparent horizon; we show that for generic metrics the deformations in the Isenberg-Mazzeo-Pollack gluings can be localised, so that the initial data on the connected sum manifold coincide with the original ones except for a small neighborhood of the gluing region; we prove existence of asymptotically flat solutions which are static or stationary up to r^{−m} terms, with arbitrary m, and with multipole moments freely prescribable within certain ranges.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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