A Course in Metric Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Metric Geometry write by Dmitri Burago. This book was released on 2001. A Course in Metric Geometry available in PDF, EPUB and Kindle. "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).
A Course in Metric Geometry
A Course in Metric Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Metric Geometry write by Dmitri Burago. This book was released on 2022-01-27. A Course in Metric Geometry available in PDF, EPUB and Kindle. “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.
Geometry
Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry write by Richard S. Millman. This book was released on 1993-05-07. Geometry available in PDF, EPUB and Kindle. Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.
An Invitation to Alexandrov Geometry
An Invitation to Alexandrov Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Alexandrov Geometry write by Stephanie Alexander. This book was released on 2019-05-08. An Invitation to Alexandrov Geometry available in PDF, EPUB and Kindle. Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Metric Structures in Differential Geometry
Metric Structures in Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metric Structures in Differential Geometry write by Gerard Walschap. This book was released on 2012-08-23. Metric Structures in Differential Geometry available in PDF, EPUB and Kindle. This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
