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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Metric Structures for Riemannian and Non-Riemannian Spaces
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Metric Structures for Riemannian and Non-Riemannian Spaces
Mikhail Gromov (Unbekannter Einband, Englisch)
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Beschreibung
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 bibliographyand index round out this unique and beautiful book. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
02.06.2010
Sprache
Englisch
EAN
9780817645823
Herausgeber
Birkhäuser Boston
Serien- oder Bandtitel
Modern Birkhäuser Classics
Sonderedition
Nein
Autor
Mikhail Gromov
Seitenanzahl
586
Einbandart
Broschiert
Übersetzt von
S. M. Bates
Schlagwörter
Algebraic topology, Homotopy, Mathematics, Probability theory, Riemannian geometry, Structures, Systole, Volume, curvature, diff.geometry, differential equation, homotopy theory, manifold, manifolds, minimum
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBP - Topologie
PBPD - Algebraische Topologie
PBKL - Integralrechnung und -gleichungen
PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.6 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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