Download or read book Computational Conformal Geometry written by Xianfeng David Gu and published by . This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Harmonic Mappings in the Plane written by Peter Duren and published by Cambridge University Press. This book was released on 2004-03-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

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 Univalent Functions and Teichm ller Spaces written by O. Lehto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in 1982. The book presumably would never have been written without Fred Gehring's continuous encouragement. Thanks to the arrangements made by Edgar Reich and David Storvick, I was able to spend the fall term of 1982 in Minneapolis and do a good part of the writing there. Back in Finland, other commitments delayed the completion of the text. At the final stages of preparing the manuscript, I was assisted first by Mika Seppala and then by Jouni Luukkainen, who both had a grant from the Academy of Finland. I am greatly indebted to them for the improvements they made in the text. I also received valuable advice and criticism from Kari Astala, Richard Fehlmann, Barbara Flinn, Fred Gehring, Pentti Jarvi, Irwin Kra, Matti Lehtinen, I1ppo Louhivaara, Bruce Palka, Kurt Strebel, Kalevi Suominen, Pekka Tukia and Kalle Virtanen. To all of them I would like to express my gratitude. Raili Pauninsalo deserves special thanks for her patience and great care in typing the manuscript. Finally, I thank the editors for accepting my text in Springer-Verlag's well known series. Helsinki, Finland June 1986 Olli Lehto Contents Preface. ... v Introduction ...

Download or read book Quasiconformal Surgery in Holomorphic Dynamics written by Bodil Branner and published by Cambridge University Press. This book was released on 2014-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.

Download or read book Quasiconformal Teichmuller Theory written by Frederick P. Gardiner and published by American Mathematical Soc.. This book was released on 2000 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Teichmüller space T(X) is the space of marked conformal structures on a given quasiconformal surface X. This volume uses quasiconformal mapping to give a unified and up-to-date treatment of T(X). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.

Download or read book Lectures on Quasiconformal Mappings written by Lars Valerian Ahlfors and published by American Mathematical Soc.. This book was released on 2006-07-14 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Download or read book Lipman Bers a Life in Mathematics written by Linda Keen and published by American Mathematical Soc.. This book was released on 2015-09-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.

Download or read book Quasiconformal Mappings and Analysis written by Peter Duren and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Download or read book Advances in the Theory of Riemann Surfaces written by Lars Valerian Ahlfors and published by Princeton University Press. This book was released on 1971-07-21 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

Download or read book Mathematical Tools for One Dimensional Dynamics written by Edson de Faria and published by Cambridge University Press. This book was released on 2008-10-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.

Download or read book Fields Medallists Lectures written by Michael Atiyah and published by World Scientific. This book was released on 1997-10-13 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.

Download or read book Boundary Behaviour of Conformal Maps written by Christian Pommerenke and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.

Download or read book 4 manifolds written by Selman Akbulut and published by Oxford University Press. This book was released on 2016 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.

Download or read book New Trends in One Dimensional Dynamics written by Maria José Pacifico and published by Springer Nature. This book was released on 2019-12-14 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016. Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo’s co-authors and former doctoral students. Sadly, Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field.

Download or read book Mathematicians of the World Unite written by Guillermo Curbera and published by CRC Press. This book was released on 2009-02-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int