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Zusatztext This impressive new book is first and foremost an original and thought-provoking contribution to the study of cosmology in research monograph form, in the best tradition of the kind of deep mathematical work which has played a crucial role in the development of the subject. Informationen zum Autor Hans Ringström obtained his PhD in 2000 at the Royal Institute of Technology in Stockholm. He spent 2000-2004 as a post doc in the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute. In 2004 he returned to Stockholm as a research assistant. In 2007 he became a Royal Swedish Academy of Sciences Research Fellow, supported by a grant from the Knut and Alice Wallenberg Foundation, a position which lasted until 2012. In 2011, Ringström obtained an associate professorship at the Royal Institute of Technology. Klappentext A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations. Zusammenfassung A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations. Inhaltsverzeichnis I Prologue 1: Introduction 2: The Initial Value Problem 3: The Topology of the Universe 4: Notions of Proximity 5: Observational Support 6: Concluding Remarks II Introductory Material 7: Main Results 8: Outline, General Theory 9: Outline, Main Results 10: References and Outlook III Background and Basic Constructions 11: Basic Analysis Estimates 12: Linear Algebra 13: Coordinates IV Function Spaces, Estimates 14: Function Spaces, Distribution Functions 15: Function Spaces on Manifolds 16: Main Weighted Estimate 17: Concepts of Convergence V Local Theory 18: Uniqueness 19: Local Existence 20: Stability VI The Cauchy Problem in General Relativity 21: The Vlasov Equation 22: The Initial Value Problem 23: Existence of an MGHD 24: Cauchy Stability VII Spatial Homogeneity 25: Spatially Homogeneous Metrics 26: Criteria Ensuring Global Existence 27: A Positive Non-Degenerate Minimum 28: Approximating Fluids VIII Future Global Non-Linear Stability 29: Background Material 30: Estimates for the Vlasov Matter 31: Global Existence 32: Asymptotics 33: Proof of the Stability Results 34: Models with Arbitrary Spatial Topology IX Appendices A: Pathologies B: Quotients and Universal Covering Spaces C: Spatially Homogeneous and Isotropic Metrics D: Auxiliary Computations in Low Regularity E: Curvature, Left Invariant Metrics F: Comments, Einstein-Boltzmann ...
