G. Galloway

Title: Global Lorentzian Geometry and the Einstein Equations

Abstract: Those lectures will focus on null objects in Lorentzian geometry, such as null geodesics, and null hypersurfaces, and their usefulness in the study of the vacuum Einstein equations.

1. Part I
   • Causal theory
   • Geometry of smooth null hypersurfaces
   • Maximum Principle for smooth null hypersurfaces
2. Part II
   • Achronal boundaries
   • $C^0$ null hypersurfaces
   • Maximum Principle for $C^0$ null hypersurfaces
   • The null splitting theorem
3. Part III - Applications
   • Uniqueness results for asymptotically de Sitter and asymptotically flat solutions of the vacuum Einstein equations
   • Results on the topology of asymptotically de Sitter solutions of the Einstein equations

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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and G. Galloway