**Graduate Studies in Mathematics**

Volume: 33;
2001;
415 pp;
Hardcover

MSC: Primary 51;

Print ISBN: 978-0-8218-2129-9

Product Code: GSM/33

List Price: $53.00

AMS Member Price: $42.40

MAA member Price: $47.70

**Electronic ISBN: 978-1-4704-1794-9
Product Code: GSM/33.E**

List Price: $53.00

AMS Member Price: $42.40

MAA member Price: $47.70

# A Course in Metric Geometry

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*Dmitri Burago; Yuri Burago; Sergei Ivanov*

“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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## A Course in Metric Geometry

- Cover Cover11 free
- Other titles in this series i2 free
- Title page v6 free
- Contents vii8 free
- Preface xi12 free
- Metric Spaces 116 free
- Length Spaces 2540
- Constructions 5974
- Spaces of Bounded Curvature 101116
- Smooth Length Structures 135150
- Curvature of Riemannian Metrics 209224
- Space of Metric Spaces 241256
- Large-scale Geometry 271286
- Spaces of Curvature Bounded Above 307322
- Spaces of Curvature Bounded Below 351366
- Bibliography 405420
- Index 409424 free
- Back Cover Back Cover1434