M. Anderson

Title: Cheeger-Gromov theory and applications to general relativity

Abstract: These lectures survey aspects of the convergence and degeneration of Riemannian metrics on a given manifold M, and some recent applications of this theory to general relativity. The basic point of view of convergence/degeneration described here originates in the work of Gromov, with subsequent work by Cheeger, and Cheeger and Gromov.

Background: Examples and Definitions.
Convergence/Compactness.
Collapse/Formation of Cusps.
Applications to Static and Stationary Space-Times.
Lorentzian Analogues and Open Problems.
Future Asymptotics and Geometrization of 3-Manifolds.

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*Second lecture*							-	-
*Third lecture*							-	-
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*Lecture notes*	-	-	-	-

Lecture notes posted on 28.VIII.2002; you might wish to check for the latest version on http://xxx.lanl.gov/abs/gr-qc/0208079

Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and M. Anderson