|
|
libcats.org
A Course in Metric GeometryDmitri Burago; Yuri Burago; and Sergei IvanovMetric 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.
Популярные книги за неделю:
Agile Principles, Patterns, and Practices in C#Автор: Robert C. Martin, Автор: Micah Martin
Размер книги: 7.18 Mb
Система упражнений по развитию способностей человека (Практическое пособие)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 818 Kb
Сотворение мира (3-х томник)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 817 Kb
Только что пользователи скачали эти книги:
Exports, Foreign Direct Investment and Economic Development in ChinaАвтор: Xiaolan FuКатегория: Экономика
Размер книги: 999 Kb
The Future of the World's Climate, Second EditionАвтор: Henderson-Sellers A., Автор: McGuffie K. (eds.)Категория: P_Physics, PGp_Geophysics
Размер книги: 34.29 Mb
|
|
|