Course in Metric Geometry
Regular price
€88.99
A01=Dmitri Burago
A01=Sergei Ivanov
A01=Yuri Burago
Author_Dmitri Burago
Author_Sergei Ivanov
Author_Yuri Burago
Category=PBM
eq_isMigrated=1
eq_isMigrated=2
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Product details
- ISBN 9781470468538
- Publication Date: 30 Jan 2001
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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 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.
Dmitri Burago, Pennsylvania State University, University Park, PA.
Yuri Burago, Steklov Institute of Mathematics, St. Petersburg, Russia.
Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia.
Yuri Burago, Steklov Institute of Mathematics, St. Petersburg, Russia.
Sergei Ivanov, Steklov Institute of Mathematics, St. Petersburg, Russia.
