Metric Spaces Convexity And Nonpositive Curvature
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Metric Spaces Convexity And Nonpositive Curvature
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2005
Metric Spaces Convexity And Nonpositive Curvature written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
Metric Spaces Convexity And Nonpositive Curvature Second Edition
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Author :
language : en
Publisher:
Release Date : 2014
Metric Spaces Convexity And Nonpositive Curvature Second Edition written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Metric Spaces Of Non Positive Curvature
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Author : Martin R. Bridson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-20
Metric Spaces Of Non Positive Curvature written by Martin R. Bridson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-20 with Mathematics categories.
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.
Lectures On Spaces Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Spaces Of Nonpositive Curvature written by Werner Ballmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Metric Spaces Of Non Positive Curvature
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Author : Martin R. Bridson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Metric Spaces Of Non Positive Curvature written by Martin R. Bridson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The purpose of this book is to describe the global properties of complete simply connected spaces that are non-positively curved in the sense of A. D. Alexandrov and to examine the structure of groups that act properly on such spaces by isometries. Thus the central objects of study are metric spaces in which every pair of points can be joined by an arc isometric to a compact interval of the real line and in which every triangle satisfies the CAT(O) inequality. This inequality encapsulates the concept of non-positive curvature in Riemannian geometry and allows one to reflect the same concept faithfully in a much wider setting - that of geodesic metric spaces. Because the CAT(O) condition captures the essence of non-positive curvature so well, spaces that satisfy this condition display many of the elegant features inherent in the geometry of non-positively curved manifolds. There is therefore a great deal to be said about the global structure of CAT(O) spaces, and also about the structure of groups that act on them by isometries - such is the theme of this book. 1 The origins of our study lie in the fundamental work of A. D. Alexandrov .
Image And Video Technology Psivt 2013 Workshops
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Author : Fay Huang
language : en
Publisher: Springer
Release Date : 2014-01-21
Image And Video Technology Psivt 2013 Workshops written by Fay Huang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-21 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the four workshops on Photographic Aesthetics and Non-Photorealistic Rendering (PAESNPR13), Geometric Properties from Incomplete Data (GPID), Quality Assessment and Control by Image and Video Analysis (QACIVA) and Geometric Computation for Computer Vision (GCCV2013), held in conjunction with the 6th Pacific-Rim Symposium on Image and Video Technology (PSIVT) in Guanajuato, Mexico during October 28-November 1, 2013. The 38 revised full papers presented were carefully selected from numerous submissions and cover all aspects of Imaging and Graphics Hardware and Visualization, Image/Video Coding and Transmission; Processing and Analysis; Retrieval and Scene Understanding, but also Applications of Image and Video Technology, Biomedical Image Processing and Analysis, Biometrics and Image Forensics, Computational Photography and Arts, Computer and Robot Vision, Pattern Recognition and Video Surveillance.
Riemannian Geometry And Geometric Analysis
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-28
Riemannian Geometry And Geometric Analysis written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-28 with Mathematics categories.
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews "...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Gradient Flows
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-29
Gradient Flows written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-29 with Mathematics categories.
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.
Measurement With Persons
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Author : Birgitta Berglund
language : en
Publisher: Psychology Press
Release Date : 2013-05-13
Measurement With Persons written by Birgitta Berglund and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Psychology categories.
Measurements with persons are those in which human perception and interpretation are used for measuring complex, holistic quantities and qualities, which are perceived by the human brain and mind. Providing means for reproducible measurement of parameters such as pleasure and pain has important implications in evaluating all kind of products, services, and conditions. This book inaugurates a new era for this subject: a multi- and inter-disciplinary volume in which world-renowned scientists from the psychological, physical, biological, and social sciences reach a common understanding of measurement theory and methods. In the first section, generic theoretical and methodological issues are treated, including the conceptual basis of measurement in the various fields involved; the development of formal, representational, and probabilistic theories; the approach to experimentation; and the theories, models, and methods for multidimensional problems. In the second section, several implementation areas are presented, including sound, visual, skin, and odor perception, functional brain imagining, body language and emotions, and, finally, the use of measurements in decision making Measurement with Persons will appeal to a wide audience across a range of sciences, including general psychology and psychophysics, measurement theory, metrology and instrumentation, neurophysiology, engineering, biology, and chemistry.