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Metric structures for Riemannian and non-Riemannian spaces

Author: Mikhael Gromov
Publisher: Boston : Birkhäuser, ©2007.
Series: Modern Birkhäuser classics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Gromov, Mikhael, 1943-
Metric structures for Riemannian and non-Riemannian spaces.
Boston : Birkhäuser, ©2007
(DLC) 2006937425
(OCoLC)86109653
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mikhael Gromov
ISBN: 9780817645830 0817645837 9780817645823 0817645829
OCLC Number: 184984815
Description: 1 online resource (xix, 585 pages) : illustrations.
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.
Series Title: Modern Birkhäuser classics.
Other Titles: Structures métriques pour les variétés Riemanniennes.
Responsibility: Misha Gromov ; with appendices by M. Katz, P. Pansu, and S. Semmes ; English translation by Sean Michael Bates.
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This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress.  Read more...

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From the reviews:"The book gives genius insight into the connections between topology and Riemannian geometry, geometry and probability, geometry and analysis, respectively. The huge variety of Read more...

 
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