A Course in Metric Geometry
Dmitri Burago author Yuri Burago author Sergei Ivanov author
Format:Paperback
Publisher:American Mathematical Society
Published:30th Jan '01
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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 the exposition.
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
ISBN: 9781470468538
Dimensions: unknown
Weight: unknown
415 pages