The Resource Metric Structures for Riemannian and Non-Riemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)

Metric Structures for Riemannian and Non-Riemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)

Label
Metric Structures for Riemannian and Non-Riemannian Spaces
Title
Metric Structures for Riemannian and Non-Riemannian Spaces
Statement of responsibility
by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu
Creator
Contributor
Author
Author
Editor
Editor
Subject
Language
  • eng
  • eng
Summary
Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. The structural metric approach to the Riemannian category, tracing back to Cheeger's thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same period, Banach spaces and probability theory underwent a geometric metamorphosis, stimulated by the Levy–Milman concentration phenomenon, encompassing the law of large numbers for metric spaces with measures and dimensions going to infinity. The first stages of the new developments were presented in Gromov's course in Paris, which turned into the famous "Green Book" by Lafontaine and Pansu (1979). The present English translation of that work has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices—by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures—as well as an extensive bibliography and index round out this unique and beautiful book
Member of
http://library.link/vocab/creatorName
Gromov, Mikhail
Dewey number
516.362
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
_kppQAijlKI
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsedt
  • Z_jCIFjv3QA
  • 9ijPHsazZgI
Language note
English
LC call number
QA641-670
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • LaFontaine, Jacques.
  • Pansu, Pierre.
Series statement
Modern Birkhäuser Classics,
http://library.link/vocab/subjectName
  • Global differential geometry
  • Cell aggregation
  • Algebraic topology
  • Mathematics
  • Global analysis (Mathematics)
  • Differential Geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Algebraic Topology
  • Measure and Integration
  • Analysis
Label
Metric Structures for Riemannian and Non-Riemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
Instantiates
Publication
Note
"Reprint of the 2001 edition."
Bibliography note
Includes bibliographical references (p. [545]-574) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Preface to the French Edition -- Preface to the English Edition -- Introduction: Metrics Everywhere -- Length Structures: Path Metric Spaces -- Degree and Dilatation -- Metric Structures on Families of Metric Spaces -- Convergence and Concentration of Metrics and Measures -- Loewner Rediscovered -- Manifolds with Bounded Ricci Curvature -- Isoperimetric Inequalities and Amenability -- Morse Theory and Minimal Models -- Pinching and Collapse -- Appendix A: 'Quasiconvex' Domains in Rn -- Appendix B: Metric Spaces and Mappings Seen at Many Scales -- Appendix C: Paul Levy's Isoperimetric Inequality -- Appendix D: Systolically Free Manifolds -- Bibliography -- Glossary of Notation -- Index
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (602 p.)
Form of item
online
Isbn
9781281377142
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-4583-0
Specific material designation
remote
System control number
  • (CKB)1000000000412336
  • (EBL)372265
  • (OCoLC)184984815
  • (SSID)ssj0000202026
  • (PQKBManifestationID)11183750
  • (PQKBTitleCode)TC0000202026
  • (PQKBWorkID)10246030
  • (PQKB)10888995
  • (DE-He213)978-0-8176-4583-0
  • (MiAaPQ)EBC372265
  • (EXLCZ)991000000000412336
Label
Metric Structures for Riemannian and Non-Riemannian Spaces, by Mikhail Gromov ; edited by Jacques LaFontaine, Pierre Pansu, (electronic resource)
Publication
Note
"Reprint of the 2001 edition."
Bibliography note
Includes bibliographical references (p. [545]-574) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Preface to the French Edition -- Preface to the English Edition -- Introduction: Metrics Everywhere -- Length Structures: Path Metric Spaces -- Degree and Dilatation -- Metric Structures on Families of Metric Spaces -- Convergence and Concentration of Metrics and Measures -- Loewner Rediscovered -- Manifolds with Bounded Ricci Curvature -- Isoperimetric Inequalities and Amenability -- Morse Theory and Minimal Models -- Pinching and Collapse -- Appendix A: 'Quasiconvex' Domains in Rn -- Appendix B: Metric Spaces and Mappings Seen at Many Scales -- Appendix C: Paul Levy's Isoperimetric Inequality -- Appendix D: Systolically Free Manifolds -- Bibliography -- Glossary of Notation -- Index
Dimensions
unknown
Edition
1st ed. 2007.
Extent
1 online resource (602 p.)
Form of item
online
Isbn
9781281377142
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-4583-0
Specific material designation
remote
System control number
  • (CKB)1000000000412336
  • (EBL)372265
  • (OCoLC)184984815
  • (SSID)ssj0000202026
  • (PQKBManifestationID)11183750
  • (PQKBTitleCode)TC0000202026
  • (PQKBWorkID)10246030
  • (PQKB)10888995
  • (DE-He213)978-0-8176-4583-0
  • (MiAaPQ)EBC372265
  • (EXLCZ)991000000000412336

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