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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
A Course in Metric Geometry
Softcover ISBN:  978-1-4704-6853-8
Product Code:  GSM/33.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-1794-9
Product Code:  GSM/33.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6853-8
eBook: ISBN:  978-1-4704-1794-9
Product Code:  GSM/33.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
A Course in Metric Geometry
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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
Softcover ISBN:  978-1-4704-6853-8
Product Code:  GSM/33.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-1794-9
Product Code:  GSM/33.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6853-8
eBook ISBN:  978-1-4704-1794-9
Product Code:  GSM/33.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    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.

    Readership

    Advanced 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. Large-scale 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 Mathematiker-Vereinigung
  • Requests
     
     
    Review Copy – for publishers of book reviews
    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.

Readership

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. 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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.