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A Course in Metric Geometry

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
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Softcover ISBN: 978-1-4704-6853-8
Product Code: GSM/33.S
List Price: $57.00 MAA Member Price:$51.30
AMS Member Price: $45.60 Electronic ISBN: 978-1-4704-1794-9 Product Code: GSM/33.E List Price:$53.00
MAA Member Price: $47.70 AMS Member Price:$42.40
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AMS Member Price: $68.40 Click above image for expanded view A Course in Metric Geometry 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 Available Formats:  Softcover ISBN: 978-1-4704-6853-8 Product Code: GSM/33.S  List Price:$57.00 MAA Member Price: $51.30 AMS Member Price:$45.60
 Electronic ISBN: 978-1-4704-1794-9 Product Code: GSM/33.E
 List Price: $53.00 MAA Member Price:$47.70 AMS Member Price: $42.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$85.50 MAA Member Price: $76.95 AMS Member Price:$68.40
• Book Details

Volume: 332001; 415 pp
MSC: 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 Carnot-Carathéodory 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.

• 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. Large-scale Geometry
• Chapter 9. Spaces of Curvature Bounded Above
• Chapter 10. Spaces of Curvature Bounded Below

• 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 Mathematiker-Vereinigung
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 332001; 415 pp
MSC: 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 Carnot-Carathéodory 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.

• 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. Large-scale 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 Mathematiker-Vereinigung
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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