000			04507nam a22005535i 4500
001			978-0-8176-4583-0
003			DE-He213
005			20161121231125.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780817645830 _9978-0-8176-4583-0
024	7		_a10.1007/978-0-8176-4583-0 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aGromov, Mikhail. _eauthor.
245	1	0	_aMetric Structures for Riemannian and Non-Riemannian Spaces _h[electronic resource] / _cby Mikhail Gromov.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2007.
300			_aXX, 586 p. 100 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aPreface 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			_aMetric 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	_aMathematics.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aMeasure theory.
650		0	_aDifferential geometry.
650		0	_aAlgebraic topology.
650		0	_aManifolds (Mathematics).
650		0	_aComplex manifolds.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aManifolds and Cell Complexes (incl. Diff.Topology).
650	2	4	_aAlgebraic Topology.
650	2	4	_aMeasure and Integration.
650	2	4	_aAnalysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817645823
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4583-0
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c508959 _d508959