| 000 -LEADER |
|---|
| fixed length control field |
04507nam a22005535i 4500 |
| 001 - CONTROL NUMBER |
|---|
| control field |
978-0-8176-4583-0 |
| 003 - CONTROL NUMBER IDENTIFIER |
|---|
| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20161121231125.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
|---|
| fixed length control field |
cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
100301s2007 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9780817645830 |
| -- |
978-0-8176-4583-0 |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.1007/978-0-8176-4583-0 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA641-670 |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
PBMP |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT012030 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
516.36 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Gromov, Mikhail. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Metric Structures for Riemannian and Non-Riemannian Spaces |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Mikhail Gromov. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Boston, MA : |
| Name of producer, publisher, distributor, manufacturer |
Birkhäuser Boston, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2007. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XX, 586 p. 100 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
|---|
| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Modern Birkhäuser Classics |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| 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. |
|---|
| 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 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Analysis (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Differential geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Algebraic topology. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Manifolds (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Complex manifolds. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Differential Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Manifolds and Cell Complexes (incl. Diff.Topology). |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Algebraic Topology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Measure and Integration. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Analysis. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Printed edition: |
| International Standard Book Number |
9780817645823 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Modern Birkhäuser Classics |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-8176-4583-0 |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
