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EBOOK
Author Ringström, Hans.
Title On the topology and future stability of the universe / Hans Ringström.
Imprint Oxford : Oxford University Press, 2013.

LOCATION CALL # STATUS MESSAGE
 OHIOLINK OXFORD EBOOKS    ONLINE  
View online
Author Ringström, Hans.
Series Oxford mathematical monographs
Oxford mathematical monographs.
Subject Cauchy problem.
Universe.
LOCATION CALL # STATUS MESSAGE
 OHIOLINK OXFORD EBOOKS    ONLINE  
View online
Author Ringström, Hans.
Series Oxford mathematical monographs
Oxford mathematical monographs.
Subject Cauchy problem.
Universe.
Description 1 online resource (xiv, 718 pages) : illustrations
Bibliography Note Includes bibliographical references and index.
Note Online resource; title from pdf information screen (Ebsco, viewed June 3, 2013).
Summary 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.
Contents ""Contents""; ""PART I: PROLOGUE""; ""1 Introduction""; ""1.1 General remarks on the limits of observations""; ""1.2 The standard models of the universe""; ""1.3 Approximation by matter of Vlasov type""; ""2 The Cauchy problem in general relativity""; ""2.1 The initial value problem in general relativity""; ""2.2 Spaces of initial data and associated distance concepts""; ""2.3 Minimal degree of regularity ensuring local existence""; ""2.4 On linearisations""; ""3 The topology of the universe""; ""3.1 An example of how to characterise topology by geometry""
""3.2 Geometrisation of 3-manifolds""""3.3 A vacuum conjecture""; ""4 Notions of proximity to spatial homogeneity and isotropy""; ""4.1 Almost EGS theorems""; ""4.2 On the relation between solutions with small spatial variation and spatially homogeneous solutions""; ""5 Observational support for the standard model""; ""5.1 Using observations to determine the cosmological parameters""; ""5.2 Distance measurements""; ""5.3 Supernovae observations""; ""5.4 Concluding remarks""; ""6 Concluding remarks""; ""6.1 On the technical formulation of stability""
""6.2 Notions of proximity to spatial homogeneity and isotropy""""6.3 Models of the universe with arbitrary closed spatial topology""; ""6.4 The cosmological principle""; ""6.5 Symmetry assumption""; ""PART II: INTRODUCTORY MATERIAL""; ""7 Main results""; ""7.1 Vlasov matter""; ""7.2 Scalar field matter""; ""7.3 The equations""; ""7.4 The constraint equations""; ""7.5 Previous results""; ""7.6 Background solution and intuition""; ""7.7 Drawing global conclusions from local assumptions""; ""7.8 Stability of spatially homogeneous solutions""
""7.9 Limitations on the global topology imposed by local observations""""8 Outline, general theory of the Einstein�Vlasov system""; ""8.1 Main goals and issues""; ""8.2 Background""; ""8.3 Function spaces and estimates""; ""8.4 Existence, uniqueness and stability""; ""8.5 The Cauchy problem in general relativity""; ""9 Outline, main results""; ""9.1 Spatially homogeneous solutions""; ""9.2 Stability in the n-torus case""; ""9.3 Estimates for the Vlasov matter, future global existence and asymptotics""; ""9.4 Proof of the main results""; ""10 References to the literature and outlook""
""10.1 Local existence""""10.2 Generalisations""; ""10.3 Potential improvements""; ""10.4 References to the literature""; ""PART III: BACKGROUND AND BASIC CONSTRUCTIONS""; ""11 Basic analysis estimates""; ""11.1 Terminology concerning differentiation and weak derivatives""; ""11.2 Weighted Sobolev spaces""; ""11.3 Sobolev spaces on the torus""; ""11.4 Sobolev spaces for distribution functions""; ""11.5 Sobolev spaces corresponding to a non-integer number of derivatives""; ""11.6 Basic analysis estimates""; ""11.7 Locally x-compact support""; ""12 Linear algebra""
ISBN 9780191669774 (electronic bk.)
0191669776 (electronic bk.)
9780191760235 (ebook)
0191760234 (ebook)
9780199680290 (print)
0199680299 (print)
OCLC # 846507613
Additional Format Print version 9780199680290



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