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Author : L. M. Kelly
Publisher : Springer
ISBN 13 : 3540379460
Total Pages : 257 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Geometry of Metric and Linear Spaces written by L. M. Kelly and published by Springer. This book was released on 2006-11-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ernst Snapper
Publisher : Elsevier
ISBN 13 : 1483269337
Total Pages : 456 pages
Book Rating : 4.4/5 (832 download)
Download or read book Metric Affine Geometry written by Ernst Snapper and published by Elsevier. This book was released on 2014-05-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.
Author : Martin R. Bridson
Publisher : Springer Science & Business Media
ISBN 13 : 3662124947
Total Pages : 665 pages
Book Rating : 4.6/5 (621 download)
Download or read book Metric Spaces of Non-Positive Curvature written by Martin R. Bridson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.
Author : Werner Ballmann
Publisher : Birkhäuser
ISBN 13 : 3034892403
Total Pages : 114 pages
Book Rating : 4.0/5 (348 download)
Download or read book Lectures on Spaces of Nonpositive Curvature written by Werner Ballmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
Author : Herbert Busemann
Publisher : Princeton University Press
ISBN 13 : 140088229X
Total Pages : 243 pages
Book Rating : 4.4/5 (8 download)
Download or read book Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) written by Herbert Busemann and published by Princeton University Press. This book was released on 2016-03-02 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.
Author : Dmitri Burago
Publisher : American Mathematical Soc.
ISBN 13 : 0821821296
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Course in Metric Geometry written by Dmitri Burago and published by American Mathematical Soc.. This book was released on 2001 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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).
Author : Michel Marie Deza
Publisher : Springer
ISBN 13 : 3642042953
Total Pages : 580 pages
Book Rating : 4.6/5 (42 download)
Download or read book Geometry of Cuts and Metrics written by Michel Marie Deza and published by Springer. This book was released on 2009-11-12 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
Author : Raymond W. Freese
Publisher : Nova Publishers
ISBN 13 : 9781590330197
Total Pages : 314 pages
Book Rating : 4.3/5 (31 download)
Download or read book Geometry of Linear 2-normed Spaces written by Raymond W. Freese and published by Nova Publishers. This book was released on 2001 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. M. Kelly
Publisher :
ISBN 13 : 9783662176252
Total Pages : 260 pages
Book Rating : 4.1/5 (762 download)
Download or read book The Geometry of Metric and Linear Spaces written by L. M. Kelly and published by . This book was released on 2014-01-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Gardner Bartle
Publisher : American Mathematical Soc.
ISBN 13 : 0821850571
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometry of Normed Linear Spaces written by Robert Gardner Bartle and published by American Mathematical Soc.. This book was released on 1986 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features 17 papers that resulted from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. This work is suitable for researchers and graduate students in functional analysis.
Author : Gilbert de B. Robinson
Publisher : Courier Corporation
ISBN 13 : 0486321045
Total Pages : 194 pages
Book Rating : 4.4/5 (863 download)
Download or read book Vector Geometry written by Gilbert de B. Robinson and published by Courier Corporation. This book was released on 2013-10-10 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
Author : Gerard Walschap
Publisher : Springer Science & Business Media
ISBN 13 : 0387218262
Total Pages : 235 pages
Book Rating : 4.3/5 (872 download)
Download or read book Metric Structures in Differential Geometry written by Gerard Walschap and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Mícheál O'Searcoid
Publisher : Springer Science & Business Media
ISBN 13 : 1846286271
Total Pages : 318 pages
Book Rating : 4.8/5 (462 download)
Download or read book Metric Spaces written by Mícheál O'Searcoid and published by Springer Science & Business Media. This book was released on 2006-12-26 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
Author : Werner Ballmann
Publisher : Springer Science & Business Media
ISBN 13 : 1468491598
Total Pages : 280 pages
Book Rating : 4.4/5 (684 download)
Download or read book Manifolds of Nonpositive Curvature written by Werner Ballmann and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collège de France in Paris. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank.
Author : S. Kumaresan
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842652503
Total Pages : 172 pages
Book Rating : 4.6/5 (525 download)
Download or read book Topology of Metric Spaces written by S. Kumaresan and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 376438722X
Total Pages : 333 pages
Book Rating : 4.7/5 (643 download)
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Author : Juha Heinonen
Publisher : Cambridge University Press
ISBN 13 : 1107092345
Total Pages : 447 pages
Book Rating : 4.1/5 (7 download)
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
