
A Course in Metric Geometry
American Mathematical Society (Publisher)
Will be published approx. on 30. January 2001
Book
Paperback/Softback
415 pages
978-1-4704-6853-8 (ISBN)
Description
Metric geometry'' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.
The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ""easy-to-touch'' mathematical objects using ""easy-to-visualize'' methods.
The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ""easy-to-touch'' mathematical objects using ""easy-to-visualize'' methods.
The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
Reviews / Votes
The book is well worth reading. Contributing to this are the many elementary examples with which the authors supplement the text ... Anyone who is intensely concerned with Riemannian geometry will not pass up this book. It is so far without competition and fills a gap in the market."" - Translated from Jahresbericht der Deutschen Mathematiker-VereinigungMore details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-6853-8 (9781470468538)
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Schweitzer Classification
Persons
Dmitri Burago, Pennsylvania State University, University Park, PA.
Yuri Burago, Steklov Institute of Mathematics, St. Petersburg, Russia.
Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia.
Yuri Burago, Steklov Institute of Mathematics, St. Petersburg, Russia.
Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia.
Content
Metric Spaces
Length Spaces
Constructions
Spaces of Bounded Curvature
Smooth Length Structures
Curvature of Riemannian Metrics
Space of Metric Spaces
Large-scale Geometry
Spaces of Curvature Bounded Above
Spaces of Curvature Bounded Below
Bibliography
Index
Length Spaces
Constructions
Spaces of Bounded Curvature
Smooth Length Structures
Curvature of Riemannian Metrics
Space of Metric Spaces
Large-scale Geometry
Spaces of Curvature Bounded Above
Spaces of Curvature Bounded Below
Bibliography
Index