On the Topology and Future Stability of the Universe

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  • Format: Hardcover
  • Copyright: 7/18/2013
  • Publisher: Oxford University Press
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Author Biography

Hans Ringstrom, Associate Professor, Department of Mathematics, KTH Royal Institute of Technology, Sweden

Hans Ringstrom 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, Ringstrom obtained an associate professorship at the Royal Institute of Technology.

Table of Contents

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

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