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Metric Structures For Riemannian And Non Riemannian Spaces

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Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-20

Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-20 with Mathematics categories.

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.

Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhael Gromov
language : en
Publisher:
Release Date : 1998

Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhael Gromov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Riemannian manifolds categories.

Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhail Gromov
language : en
Publisher: Birkhäuser
Release Date : 2006-12-22

Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-22 with Mathematics categories.

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.

Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25

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.

Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhail Gromov
language : en
Publisher: Birkhäuser
Release Date : 2008-11-01

Geometric Possibility

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Author : Gordon Belot
language : en
Publisher: OUP Oxford
Release Date : 2011-04-28

Geometric Possibility written by Gordon Belot and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-28 with Science categories.

Relationalism about space is a venerable doctrine that is enjoying renewed attention among philosophers and physicists. Relationalists deny that space is ontologically prior to matter and seek to ground all claims about the structure of space in facts about actual and possible configurations of matter. Thus, many relationalists maintain that to say that space is infinite is to say that certain sorts of infinite arrays of material points are possible (even if, in fact, the world contains only a finite amount of matter). Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of nature, modal notions, or more general issues in ontology.

Non Doubling Ahlfors Measures Perimeter Measures And The Characterization Of The Trace Spaces Of Sobolev Functions In Carnot Caratheodory Spaces

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Author : Donatella Danielli
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Non Doubling Ahlfors Measures Perimeter Measures And The Characterization Of The Trace Spaces Of Sobolev Functions In Carnot Caratheodory Spaces written by Donatella Danielli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Caratheodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on a lower dimensional manifold, and which satisfies an Ahlfors type condition with respect to the standard Lebesgue measure. We also study the extension problem for the relevant Besov spaces. Various concrete applications to the setting of Carnot groups are analyzed in detail and an application to the solvability of the subelliptic Neumann problem is presented.

Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance

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Author : Marc Aristide Rieffel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance written by Marc Aristide Rieffel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di

Elliptic Pdes On Compact Ricci Limit Spaces And Applications

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Author : Shouhei Honda
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

Elliptic Pdes On Compact Ricci Limit Spaces And Applications written by Shouhei Honda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.

In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.

Metric Structures In Differential Geometry

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Author : Gerard Walschap
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-18

Metric Structures In Differential Geometry written by Gerard Walschap and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-18 with Mathematics categories.

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

Metric Structures For Riemannian And Non Riemannian Spaces

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