MARC details
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03595cam a2200241 a 4500 |
| 001 - CONTROL NUMBER |
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vtls000001793 |
| 003 - CONTROL NUMBER IDENTIFIER |
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VRT |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20250102224545.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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081110s1999 maua |b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
0817638989 (acidfree paper) |
| 039 #9 - LEVEL OF BIBLIOGRAPHIC CONTROL AND CODING DETAIL [OBSOLETE] |
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| Level of rules in bibliographic description |
201402040100 |
| Level of effort used to assign nonsubject heading access points |
VLOAD |
| Level of effort used to assign subject headings |
201007271208 |
| Level of effort used to assign classification |
malmash |
| Level of effort used to assign subject headings |
200811101326 |
| Level of effort used to assign classification |
venkatrajand |
| Level of effort used to assign subject headings |
200811100852 |
| Level of effort used to assign classification |
Noora |
| -- |
200811100851 |
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Noora |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA649 |
| Item number |
.G8313 1999 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Gromov, Mikhael, |
| Dates associated with a name |
1943- |
| 9 (RLIN) |
43675 |
| 240 10 - UNIFORM TITLE |
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| Uniform title |
English |
| 245 10 - TITLE STATEMENT |
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| Title |
Metric Structures for Riemannian and Non-Riemannian Spaces / |
| Statement of responsibility, etc. |
Mikhail Gromov ; English translation by Sean Michael Bates ; with appendices by M. Katz, P. Pansu, and S. Semmes. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Boston : |
| Name of publisher, distributor, etc. |
Birkhauser, |
| Date of publication, distribution, etc. |
c1999. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xix, 585 p. : |
| Other physical details |
ill. ; |
| Dimensions |
25 cm. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes bibliographical references (p. [545]-574) and index. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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 appendicesoby 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 measuresoas well as an extensive bibliography and index round out this unique an |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Riemannian manifolds. |
| 9 (RLIN) |
43676 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Library of Congress Classification |
| Suppress in OPAC |
No |
| Koha item type |
Books |
