Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces  
Author(s) Misha Gromov
Country United States
Language English
Genre(s) Mathematics
Publisher Birkhäuser Boston, Inc.
Publication date 1999
Media type Print
Pages xx+585 pp
ISBN 0-8176-3898-9


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 publisher CEDIC, Paris. The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu. The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz. Since then, the book was reprinted several times.

Contents

Reviews

Reviewer Igor Belegradek for MathSciNet wrote that the book

is considered one of the most influential books in geometry in the last twenty years. Since then the boundary of the field has dramatically exploded. Reflecting this growth, the new English edition has almost quadrupled in size.[1]

Reviewer Mircea Craioveanu for Zentralblatt wrote:

This book will become one of the standard references in the research literature on the subject. Many fascinating open problems are pointed out. Since this domain has dramatically exploded since 1979 and also is one which has many contact points with diverse areas of mathematics, it is no small task to present a treatment which is at once broad and coherent. It is a major accomplishment of Misha Gromov to have written this exposition.[2]

Contents

Notes

  1. ^ See http://www.ams.org/mathscinet-getitem?mr=1699320
  2. ^ See http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:0953.53002&format=complete
v · Systolic geometry
1-systoles of surfaces
1-systoles of manifolds
Higher systoles
Gromov's inequality for complex projective space · Systolic freedom · Systolic category

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