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by Mikhail Gromov,Jacques LaFontaine,Pierre Pansu,S. M. Bates,M. Katz,P. Pansu,S. Semmes

Download Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics) fb2
Author: Mikhail Gromov,Jacques LaFontaine,Pierre Pansu,S. M. Bates,M. Katz,P. Pansu,S. Semmes
ISBN: 0817645829
Language: English
Pages: 586 pages
Category: Mathematics
Publisher: Birkhäuser; 1st ed. 1999. Corr. 2nd printing 2001. 3rd printing 2006 edition (December 22, 2006)
Rating: 4.9
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FB2 size: 1778 kb | EPUB size: 1127 kb | DJVU size: 1156 kb
Sub: Math

ISBN-13: 978-0817645823. this work will continue to set the standard in the field for the foreseeable future. M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (4), April, 2009).

The structural metric approach to the Riemannian category, tracing back to. .

The structural metric approach to the Riemannian category, tracing back to Cheegers thesis, pivots around the notion of the Gromov-Hausdorff distance between Riemannian manifolds. 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

Pierre Pansu Departement de Mathematiques Universite de Paris-Sud 91405 Orsay Cedex, France.

Pierre Pansu Departement de Mathematiques Universite de Paris-Sud 91405 Orsay Cedex, France. ISBN 0-8176-3898-9 (acid-free paper) 1. Riemannian manifolds.

Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by CEDIC (Paris). The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz.

and Non-riemannian Spaces Marcel Proust, Le temps retrouv ée D e fi ni t i o n.Riemannian Geometry: A Modern Introduction.

and Non-riemannian Spaces Marcel Proust, Le temps retrouv ée D e fi ni t i o n: A m e t ri c s.Metric Structures for Riemannian and Non-Riemannian Spaces. 76 MB·13 Downloads·New! was followed by the creation of the asymptotic metric theory of infinite groups by Gromov. 22 MB·1,416 Downloads. Cambridge studies in advanced mathematics.

Pierre Pansu is a French mathematician and a member of the Arthur Besse group and a close collaborator of Mikhail Gromov. He is a professor at the Université Paris-Sud 11 and the École Normale Supérieure in Paris. His contribution to mathematics is being celebrated by a double event co-organized for his 60th birthday by the Clay Mathematics Institute. Stephen Semmes is the Noah Harding Professor of Mathematics at Rice University.

Mikhail Gromov, M. Katz, P. P.Created by an anonymous user.Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Bir. Are you sure you want to remove Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics) from your list? Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics). Published December 22, 2006 by Birkhäuser Boston.

Modern Birkha?user classics.

Metric structures for Riemannian and non-Riemannian spaces Misha Gromov ; with appendices by M. Pansu, and S. Semmes ; English translation by Sean Michael Bates. Library of Congress Control Number: 2006937425. Modern Birkha?user classics. Bibliography, etc. Note: Includes bibliographical references (p. -574) and index. Download book Metric structures for Riemannian and non-Riemannian spaces, Misha Gromov ; with appendices by M.

Find many great new & used options and get the best deals for Metric Structures for Riemannian and Non-riemannian . This book is an English translation of the famous Green Book by Lafontaine and Pansu (1979).

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.

and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by publisher CEDIC, Paris. Appendix A, by Pierre Pansu, deals with quasiconvex domains in Euclidean space. Appendix B, by Stephen Semmes, deals with metric spaces and mappings seen from within.

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.

Comments (4)
Silly Dog
The cover was a little bit wrinkled.
Marilbine
The french version (written by Pierre Pansu, based on Gromov's lectures) is a jewel which gives a perfect introduction to the subject (not too much detail, a lot of insight, etc). The new parts (chapter 3.5, Semmes' supplement) really unbalance the book, though if you think of them as Volume 2, the changes might be palatable...
Conjukus
Formally speaking, this is the second edition of a set of Paris lecture notes published by Gromov two decades ago in the French language. However, such a wealth of entirely new material has been added that in essence we are talking of a new book.
Among the additions, the bulky new chapter 3 1/2+ stands out, dealing with the phenomenon of concentration of measure on high-dimensional structures. This is a relatively recent discovery of modern analysis and geometry, tracing its origin to the work of Paul Levy and especially Vitali Milman. The essence of the phenomenon is that on many multidimensional structures, every `nice' function is constant with high probability. The manifestations of the phenomenon are many - from geometric functional analysis (Dvoretzky theorem) through information theory (blowing-up lemma) and probability (law of large numbers) to graph theory (superconcentrators) and topological dynamics. As Gromov stresses in his book, even deeper aspects of the concentration phenomenon have been long since discovered and are constantly explored in statistical physics in the context of phase transitions of various kind, and some of the first known examples where phase transitions appear in the context of geometry have been discovered by Gromov himself, e.g. for hyperbolic groups. Finding and exploring more instances of phase transitions in mathematics might well become a unifying heuristic principle across a large number of disciplines.
The mathematical setting for dealing with concentration and related issues is the concept of a metric space equipped with finite measure, what Gromov calls an mm-space. Apart from concrete objects (such as for instance spheres and cubes), there are `higher-level' examples of mm-spaces, for instance those whose elements are isomorphism classes of mathematical objects themselves (e.g. Riemanning manifolds or finitely generated groups). This leads to a probabilistic treatment of such objects. Of course Gromov's strength is that his treatment is always concrete and he never theorizes without having particular objects and applications in mind.
It is quite safe to claim that the full range and power of applications of the interaction between metric and measure are yet to be discovered, which is what makes this book so important. It is rich in open questions and suggested new research directions, but more than that, it helps the reader to develop a good intuitive feeling of where things are going these days, what things ought to be done, and what constitutes proper mathematics.
Even though I unexpectedly found myself among the privileged ones who received a copy of the book as a gift from the author, I would have certainly purchased it otherwise, as I firmly believe that every mathematical library in the world, be it that of a top-class University or just a modest, lovingly selected office collection of a humble mathematician, will be wanting without a copy of the monograph under review, which might well become one of the most important books in mathematical sciences for the early XXIst century.
Khiceog
This book (originally published in French and improved here) is a fundamentally important book opening up an entire field of mathematics. For a textbook based on this material and related topics try Burago-Burago-Ivanov's textbook on the subject which can be taught to first year graduate students. For mathematicians and advanced graduate students, Gromov's book is a masterpiece.