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A Course in Metric Geometry
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A Course in Metric Geometry

A Course in Metric Geometry

Dmitri Burago, Yuri Burago, Sergei Ivanov

414 pages, parution le 17/12/2001

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

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