On the topology and future stability of the universe /:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford :
Oxford University Press,
2013.
|
| Schriftenreihe: | Oxford mathematical monographs.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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. |
| Beschreibung: | 1 online resource (xiv, 718 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780191669774 0191669776 9780191760235 0191760234 9780199680290 0199680299 |
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| 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 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"" | |
| 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 | |
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| adam_text | |
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| author | Ringström, Hans |
| author_facet | Ringström, Hans |
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| 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-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 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 ""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 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 |
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| discipline | Mathematik |
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| geographic | Universe. http://id.loc.gov/authorities/subjects/sh2010007248 Universe fast |
| geographic_facet | Universe. Universe |
| id | ZDB-4-EBA-ocn846507613 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:22Z |
| institution | BVB |
| isbn | 9780191669774 0191669776 9780191760235 0191760234 9780199680290 0199680299 |
| language | English |
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| series2 | Oxford mathematical monographs |
| spelling | Ringström, Hans. On the topology and future stability of the universe / Hans Ringström. Oxford : Oxford University Press, 2013. 1 online resource (xiv, 718 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Oxford mathematical monographs Includes bibliographical references and index. Online resource; title from pdf information screen (Ebsco, viewed June 3, 2013). 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 -- 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-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 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 ""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"" 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 Cauchy problem. http://id.loc.gov/authorities/subjects/sh85021438 Universe. http://id.loc.gov/authorities/subjects/sh2010007248 Problème de Cauchy. MATHEMATICS Differential Equations Partial. bisacsh Cauchy problem fast Universe fast has work: On the topology and future stability of the universe (Text) https://id.oclc.org/worldcat/entity/E39PCGJF3kK73KR8rdFCqfqGBK https://id.oclc.org/worldcat/ontology/hasWork Print version 9780199680290 Oxford mathematical monographs. http://id.loc.gov/authorities/names/n83826371 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=579031 Volltext |
| spellingShingle | Ringström, Hans On the topology and future stability of the universe / Oxford mathematical monographs. 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-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 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 ""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"" 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 Cauchy problem. http://id.loc.gov/authorities/subjects/sh85021438 Problème de Cauchy. MATHEMATICS Differential Equations Partial. bisacsh Cauchy problem fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85021438 http://id.loc.gov/authorities/subjects/sh2010007248 |
| title | On the topology and future stability of the universe / |
| title_auth | On the topology and future stability of the universe / |
| title_exact_search | On the topology and future stability of the universe / |
| title_full | On the topology and future stability of the universe / Hans Ringström. |
| title_fullStr | On the topology and future stability of the universe / Hans Ringström. |
| title_full_unstemmed | On the topology and future stability of the universe / Hans Ringström. |
| title_short | On the topology and future stability of the universe / |
| title_sort | on the topology and future stability of the universe |
| topic | Cauchy problem. http://id.loc.gov/authorities/subjects/sh85021438 Problème de Cauchy. MATHEMATICS Differential Equations Partial. bisacsh Cauchy problem fast |
| topic_facet | Cauchy problem. Universe. Problème de Cauchy. MATHEMATICS Differential Equations Partial. Cauchy problem Universe |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=579031 |
| work_keys_str_mv | AT ringstromhans onthetopologyandfuturestabilityoftheuniverse |