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


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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