　　“度量几何”是建立在拓扑空间长度概念基础之上的处理几何的方法，这种方法在*近几十年飞速发展，并渗透到诸如群论、动力系统和偏微分方程等其他数学学科。
　　《度量几何学教程（英文版）》有两个目标：详细阐述长度空间理论中使用的基本概念和技巧，以及为大量不同的几何论题提供一个初等导引，这些论题都与距离观念相关，包括黎曼度量和Carnot-Caratheodory度量、双曲平面、距离-体积不等式、（大规模的、粗糙的）渐近几何、Gromov双曲空间、度量空间的收敛性以及Alexandrov空间（非正和非负的弯曲空间）。作者倾向于用“易于看见”的方法来处理“易于触碰”的数学对象。
　　作者设定了一个具有挑战性的目标，即让《度量几何学教程（英文版）》的核心部分能为一年级研究生所接受。大多数新的概念和方法都按*简单的情形来提出并阐明，从而避免了技术性的障碍。书中还包括大量习题，这些习题是《度量几何学教程（英文版）》至关重要的一部分。

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Preface
Chapter 1． Metric Spaces
1．1． Definitions
1．2． Examples
1．3． Metrics and Topology
1．4． Lipschitz Maps
1．5． Complete Spaces
1．6． Compact Spaces
1．7． Hausdorff Measure and Dimension

Chapter 2． Length Spaces
2．1． Length Structures
2．2． First Examples of Length Structures
2．3． Length Structures Induced by Metrics
2．4． Characterization of Intrinsic Metrics
2．5． Shortest Paths
2．6． Length and Hausdorff Measure
2．7． Length and Lipschitz Speed

Chapter 3． Constructions
3．1． Locality， Gluing and Maximal Metrics
3．2． Polyhedral Spaces
3．3． Isometries and Quotients
3．4． Local Isometries and Coverings
3．5． Arcwise Isometries
3．6． Products and Cones

Chapter 4． Spaces of Bounded Curvature
4．1． Definitions
4．2． Examples
4．3． Angles in Alexandrov Spaces and Equivalence of Definitions
4．4． Analysis of Distance Functions
4．5． The First Variation Formula
4．6． Nonzero Curvature Bounds and Globalization
4．7． Curvature of Cones

Chapter 5． Smooth Length Structures
5．1． Riemannian Length Structures
5．2． Exponential Map
5．3． Hyperbolic Plane
5．4． Sub-Riemannian Metric Structures
5．5． Riemannian and Finsler Volumes
5．6． Besikovitch Inequality

Chapter 6． Curvature of Riemannian Metrics
6．1． Motivation： Coordinate Computations
6．2． Covariant Derivative
6．3． Geodesic and Gaussian Curvatures
6．4． Geometric Meaning of Gaussian Curvature
6．5． Comparison Theorems

Chapter 7． Space of Metric Spaces
7．1． Examples
7．2． Lipschitz Distance
7．3． Gromov-Hausdorff Distance
7．4． Gromov-Hausdorff Convergence
7．5． Convergence of Length Spaces

Chapter 8． Large-scale Geometry
8．1． Noncompact Gromov-Hausdorff Limits
8．2． Tangent and Asymptotic Cones
8．3． Quasi-isometries
8．4． Gromov Hyperbolic Spaces
8．5． Periodic Metrics

Chapter 9． Spaces of Curvature Bounded Above
9．1． Definitions and Local Properties
9．2． Hadamard Spaces
9．3． Fundamental Group of a Nonpositively Curved Space
9．4． Example： Semi-dispersing Billiards

Chapter 10． Spaces of Curvature Bounded Below
10．1． One More Definition
10．2． Constructions and Examples
10．3． Toponogov's Theorem
10．4． Curvature and Diameter
10．5． Splitting Theorem
10．6． Dimension and Volume
10．7． Gromov-Hausdorff Limits
10．8． Local Properties
10．9． Spaces of Directions and Tangent Cones
10．10． Further Information
Bibliography
Index
度量几何学教程（英文版） [A Course in Metric Geometry] 下载 mobi epub pdf txt 电子书格式