A Course in Metric Geometry ( Graduate Studies in Mathematics )

Publication series :Graduate Studies in Mathematics

Author: Dmitri Burago;Yuri Burago;Sergei Ivanov  

Publisher: American Mathematical Society‎

Publication year: 2001

E-ISBN: 9781470417949

P-ISBN(Hardback):  9780821821299

Subject: O189.11 topological space (topological space)

Keyword: 暂无分类

Language: ENG

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A Course in Metric Geometry

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-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.

Chapter

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Title page

Contents

Preface

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

Back Cover

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