On the topology and future stability of the universe / Hans Ringström.

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...

Full description

Saved in:
Bibliographic Details
Main Author: Ringström, Hans
Format: eBook
Language:English
Published: Oxford : Oxford University Press, 2013.
Series:Oxford mathematical monographs.
Subjects:
Online Access:Click for online access

MARC

LEADER 00000cam a2200000 a 4500
001 ocn846507613
003 OCoLC
005 20240808213014.0
006 m o d
007 cr cnu---unuuu
008 130603s2013 enka ob 001 0 eng d
040 |a N$T  |b eng  |e pn  |c N$T  |d E7B  |d YDXCP  |d STF  |d COO  |d OCLCQ  |d EBLCP  |d OCLCF  |d OCLCQ  |d STBDS  |d OCLCQ  |d YOU  |d AU@  |d OCLCQ  |d YDX  |d OCLCQ  |d OCLCO  |d SFB  |d OCLCO  |d OCLCQ  |d OCLCO  |d OCLCL 
019 |a 922971721 
020 |a 9780191669774  |q (electronic bk.) 
020 |a 0191669776  |q (electronic bk.) 
020 |a 9780191760235  |q (ebook) 
020 |a 0191760234  |q (ebook) 
020 |a 9780199680290  |q (print) 
020 |a 0199680299  |q (print) 
035 |a (OCoLC)846507613  |z (OCoLC)922971721 
050 4 |a QA377  |b .R56 2013eb 
072 7 |a MAT  |x 007020  |2 bisacsh 
049 |a HCDD 
100 1 |a Ringström, Hans. 
245 1 0 |a On the topology and future stability of the universe /  |c Hans Ringström. 
260 |a Oxford :  |b Oxford University Press,  |c 2013. 
300 |a 1 online resource (xiv, 718 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Oxford mathematical monographs 
504 |a Includes bibliographical references and index. 
588 0 |a Online resource; title from pdf information screen (Ebsco, viewed June 3, 2013). 
520 8 |a 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. 
505 0 |a 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 
505 8 |a 3.2 Geometrisation of 3-manifolds3.3 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 
505 8 |a 6.2 Notions of proximity to spatial homogeneity and isotropy6.3 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 
505 8 |a ""7.9 Limitations on the global topology imposed by local observations""""8 Outline, general theory of the Einsteinâ€?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"" 
505 8 |a 10.1 Local existence10.2 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 
650 0 |a Cauchy problem. 
651 0 |a Universe. 
650 7 |a MATHEMATICS  |x Differential Equations  |x Partial.  |2 bisacsh 
650 7 |a Cauchy problem  |2 fast 
651 7 |a Universe  |2 fast 
758 |i has work:  |a On the topology and future stability of the universe (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGJF3kK73KR8rdFCqfqGBK  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version  |z 9780199680290 
830 0 |a Oxford mathematical monographs. 
856 4 0 |u https://holycross.idm.oclc.org/login?auth=cas&url=https://academic.oup.com/book/2256  |y Click for online access 
903 |a OUP-SOEBA 
994 |a 92  |b HCD