Geometry And Dynamics In Gromov Hyperbolic Metric Spaces
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Geometry And Dynamics In Gromov Hyperbolic Metric Spaces
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Author : Tushar Das
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-14
Geometry And Dynamics In Gromov Hyperbolic Metric Spaces written by Tushar Das and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-14 with Geometry, Hyperbolic categories.
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Elements Of Asymptotic Geometry
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Author : Sergei Buyalo
language : en
Publisher: European Mathematical Society
Release Date : 2007
Elements Of Asymptotic Geometry written by Sergei Buyalo 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.
Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity. In the first part of this book, in analogy with the concepts of classical hyperbolic geometry, the authors provide a systematic account of the basic theory of Gromov hyperbolic spaces. These spaces have been studied extensively in the last twenty years and have found applications in group theory, geometric topology, Kleinian groups, as well as dynamics and rigidity theory. In the second part of the book, various aspects of the asymptotic geometry of arbitrary metric spaces are considered. It turns out that the boundary at infinity approach is not appropriate in the general case, but dimension theory proves useful for finding interesting results and applications. The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory. The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich.
Symbolic Dynamics And Hyperbolic Groups
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Author : Michel Coornaert
language : en
Publisher: Springer
Release Date : 2006-11-14
Symbolic Dynamics And Hyperbolic Groups written by Michel Coornaert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces
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Author : Lior Fishman
language : en
Publisher:
Release Date : 2018
Diophantine Approximation And The Geometry Of Limit Sets In Gromov Hyperbolic Metric Spaces written by Lior Fishman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Diophantine approximation categories.
In this paper, we provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic '76 paper to more recent results of Hersonsky and Paulin ('02, '04, '07). Concrete examples of situations we consider which have not been considered before include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which we are aware, our results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones ('97) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson-Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem.
A Course In Metric Geometry
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Author : Dmitri Burago
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-27
A Course In Metric Geometry written by Dmitri Burago and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
“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.
Conformal Dimension
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Author : John M. Mackay
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Conformal Dimension written by John M. Mackay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.
Surveys In Geometry I
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Author : Athanase Papadopoulos
language : en
Publisher: Springer Nature
Release Date : 2022-02-18
Surveys In Geometry I written by Athanase Papadopoulos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.
Bibliography On Water Requirements In Rice 1963 1950
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Author :
language : en
Publisher:
Release Date : 1963
Bibliography On Water Requirements In Rice 1963 1950 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
A Course In Metric Geometry
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Author : Dmitri Burago
language : en
Publisher: American Mathematical Soc.
Release Date :
A Course In Metric Geometry written by Dmitri Burago and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"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).
Geometry Topology And Dynamics In Negative Curvature
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Author : C. S. Aravinda
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-21
Geometry Topology And Dynamics In Negative Curvature written by C. S. Aravinda and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-21 with Mathematics categories.
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.