A Course in Metric Geometry

Dmitri Burago, Yuri Burago, Sergei Ivanov

414 pages, parution le 17/12/2001

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Résumé

"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-Caratheodory 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 exposition.

Contents

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

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Dmitri Burago, Yuri Burago, Sergei Ivanov
Parution	17/12/2001
Nb. de pages	414
Format	18 x 26
Couverture	Relié
Poids	950g
Intérieur	Noir et Blanc
EAN13	9780821821299
ISBN13	978-0-8218-2129-9