Metric Structures for Riemannian and Non-Riemannian Spaces (Progress in Mathematics, Vol. 152)

0 avg rating
( 0 ratings by Goodreads )
 
9780817638986: Metric Structures for Riemannian and Non-Riemannian Spaces (Progress in Mathematics, Vol. 152)
View all copies of this ISBN edition:
 
 

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.

"synopsis" may belong to another edition of this title.

From the Back Cover:

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.

Language Notes:

Text: English (translation)
Original Language: French

"About this title" may belong to another edition of this title.

Buy New View Book
List Price: US$ 99.00
US$ 260.05

Convert currency

Shipping: US$ 4.95
Within U.S.A.

Destination, rates & speeds

Add to Basket

Other Popular Editions of the Same Title

9780817645823: Metric Structures for Riemannian and Non-Riemannian Spaces (Modern Birkhäuser Classics)

Featured Edition

ISBN 10:  0817645829 ISBN 13:  9780817645823
Publisher: Birkhäuser, 2006
Softcover

9783764338985: Metric Structures for Riemannian and Non-Riemannian Spaces (Progress in Materials Science)

Birkha..., 1998
Hardcover

Top Search Results from the AbeBooks Marketplace

1.

Mikhail Gromov
ISBN 10: 0817638989 ISBN 13: 9780817638986
New Quantity Available: 1
Seller:
BennettBooksLtd
(San Diego, CA, U.S.A.)
Rating
[?]

Book Description Condition: New. New. Seller Inventory # STR-0817638989

More information about this seller | Contact this seller

Buy New
US$ 260.05
Convert currency

Add to Basket

Shipping: US$ 4.95
Within U.S.A.
Destination, rates & speeds

2.

Gromov, Mikhail
Published by Birkhäuser (2001)
ISBN 10: 0817638989 ISBN 13: 9780817638986
New Hardcover Quantity Available: 2
Seller:
Murray Media
(NORTH MIAMI BEACH, FL, U.S.A.)
Rating
[?]

Book Description Birkhäuser, 2001. Hardcover. Condition: New. Never used!. Seller Inventory # P110817638989

More information about this seller | Contact this seller

Buy New
US$ 266.96
Convert currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, rates & speeds