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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.
Metric Structures for Riemannian and Non-Riemannian Spaces ; Author: Mikhail Gromov: Original title: Structures métriques pour les variétés riemanniennes
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.
Jan 1, 2007 · The group of diffeomorphisms Diff(V) of a smooth manifold V naturally acts on the space of Riemannian metrics g on V; various classes of metrics one studies in geometry are usually invariant under ...
Metric structures for Riemannian and non-Riemannian spaces. Metric structures for Riemannian and non-Riemannian spaces / August 28, 2018 / Distance geometry in Riemannian manifolds, Metric invariants and quantitative topology, Metric, measure, concentration and isoperimetric inequalities
Apr 20, 2001 · 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.
Misha Gromov with Appendices by M. Katz, P. Pansu, and S. Semmes Metric Structures for Riemannian and Non-Riemannian Spaces Based on Structures Metriques des Varietes Riemanniennes
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Dec 22, 2006 · 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. 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.
Bibliography Includes bibliographical references (p. [545]-574) and index. Contents. Preface to the French Edition * Preface to the English Edition * Introduction: Metrics Everywhere *
