Download or read book Extension Theorems for Boundary Maps in Gromov Hyperbolic Spaces written by Julian Jordi and published by . This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
Download or read book Five Lectures in Complex Analysis written by Contreras Márquez Contreras and published by American Mathematical Soc.. This book was released on 2010 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains state-of-art survey papers in complex analysis based on lectures given at the second Winter School on Complex Analysis and Operator Theory held in February 2008 at the University of Sevilla, Sevilla, Spain. --
Download or read book Metrical and Dynamical Aspects in Complex Analysis written by Léa Blanc-Centi and published by Springer. This book was released on 2017-11-03 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.
Download or read book Strasbourg Master Class on Geometry written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2012 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmuller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry.
Download or read book Geometry and Dynamics in Gromov Hyperbolic Metric Spaces written by Tushar Das and published by American Mathematical Soc.. This book was released on 2017-04-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Group Theory written by Mladen Bestvina and published by American Mathematical Soc.. This book was released on 2014-12-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Download or read book Selected Works of Oded Schramm written by Itai Benjamini and published by Springer Science & Business Media. This book was released on 2011-08-12 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
Download or read book Elements of Asymptotic Geometry written by Sergei Buyalo and published by European Mathematical Society. This book was released on 2007 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Complex Analysis written by Reiner Kuhnau and published by Elsevier. This book was released on 2004-12-09 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Download or read book Uniformizing Gromov Hyperbolic Spaces written by Mario Bonk and published by Societe Mathematique De France. This book was released on 2001 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays in Group Theory written by S.M. Gersten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conformal Dimension written by John M. Mackay and published by American Mathematical Soc.. This book was released on 2010 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Expanding Thurston Maps written by Mario Bonk and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration. It is called expanding if, roughly speaking, preimages of a fine open cover of the underlying sphere under iterates of the map become finer and finer as the order of the iterate increases. Every expanding Thurston map gives rise to a fractal space, called its visual sphere. Many dynamical properties of the map are encoded in the geometry of this visual sphere. For example, an expanding Thurston map is topologically conjugate to a rational map if and only if its visual sphere is quasisymmetrically equivalent to the Riemann sphere. This relation between dynamics and fractal geometry is the main focus for the investigations in this work. The book is an introduction to the subject. The prerequisites for the reader are modest and include some basic knowledge of complex analysis and topology. The book has an extensive appendix, where background material is reviewed such as orbifolds and branched covering maps.
Download or read book Ergodic Theory and Its Connection with Harmonic Analysis written by Karl Endel Petersen and published by Cambridge University Press. This book was released on 1995 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tutorial survey papers on important areas of ergodic theory, with related research papers.
Download or read book Discrete Geometric Analysis written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2004 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.
