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The Vlasov-Einstein system describes a self-gravitating, collisionless gaswithin the framework of general relativity. We investigate the initial valueproblem in a cosmological setting with spherical, plane, or hyperbolic symmetryand prove that for small initial data solutions exist up to a spacetimesingularity which is a curvature and a crushing singularity. An important toolin the analysis is a local existence result with a continuation criterionsaying that solutions can be extended as long as the momenta in the support ofthe phase-space distribution of the matter remain bounded.Comment: 32 pages, LaTeX, report 94

Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry