A Course in Metric Geometry (The Graduate Studies in Mathematics, 33) - Softcover

Dmitri Burago; Yuri Burago; Sergei Ivanov

Softcover

ISBN 10: 1470468530 ISBN 13: 9781470468538

Publisher: American Mathematical Society, 2022

Synopsis

“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.

About this title

About the Author

Dmitri Burago, Pennsylvania State University, University Park, PA, Yuri Burago, Steklov Institute of Mathematics, St. Petersburg, Russia, and Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470468530
• ISBN 13: 9781470468538
• Binding: Paperback
• Number of pages: 415