Softcover ISBN:  9781470468538 
Product Code:  GSM/33.S 
List Price:  $57.00 
MAA Member Price:  $51.30 
AMS Member Price:  $45.60 
Electronic ISBN:  9781470417949 
Product Code:  GSM/33.E 
List Price:  $53.00 
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Book DetailsGraduate Studies in MathematicsVolume: 33; 2001; 415 ppMSC: Primary 51;
“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 CarnotCarathéodory metrics, the hyperbolic plane, distancevolume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (nonpositively and nonnegatively curved spaces). The authors tend to work with “easytotouch” mathematical objects using “easytovisualize” methods.
The authors set a challenging goal of making the core parts of the book accessible to firstyear 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.ReadershipAdvanced undergraduates, graduate students, and research mathematicians interested in geometry and specialists in related fields.

Table of Contents

Chapters

Chapter 1. Metric Spaces

Chapter 2. Length Spaces

Chapter 3. Constructions

Chapter 4. Spaces of Bounded Curvature

Chapter 5. Smooth Length Structures

Chapter 6. Curvature of Riemannian Metrics

Chapter 7. Space of Metric Spaces

Chapter 8. Largescale Geometry

Chapter 9. Spaces of Curvature Bounded Above

Chapter 10. Spaces of Curvature Bounded Below


Additional Material

Reviews

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 MathematikerVereinigung


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“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 CarnotCarathéodory metrics, the hyperbolic plane, distancevolume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (nonpositively and nonnegatively curved spaces). The authors tend to work with “easytotouch” mathematical objects using “easytovisualize” methods.
The authors set a challenging goal of making the core parts of the book accessible to firstyear 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.
Advanced undergraduates, graduate students, and research mathematicians interested in geometry and specialists in related fields.

Chapters

Chapter 1. Metric Spaces

Chapter 2. Length Spaces

Chapter 3. Constructions

Chapter 4. Spaces of Bounded Curvature

Chapter 5. Smooth Length Structures

Chapter 6. Curvature of Riemannian Metrics

Chapter 7. Space of Metric Spaces

Chapter 8. Largescale Geometry

Chapter 9. Spaces of Curvature Bounded Above

Chapter 10. Spaces of Curvature Bounded Below

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 MathematikerVereinigung