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Quadratic Differentials
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Book Synopsis Quadratic Differentials by : K. Strebel
Download or read book Quadratic Differentials written by K. Strebel and published by Springer Science & Business Media. This book was released on 1984-04-02 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse.
Book Synopsis Teichmüller Theory and Quadratic Differentials by : Frederick P. Gardiner
Download or read book Teichmüller Theory and Quadratic Differentials written by Frederick P. Gardiner and published by Wiley-Interscience. This book was released on 1987-08-11 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a unified treatment of both the modern and the classical aspects of Teichmuller theory. The classical parts of the theory include Teichmuller's theorem on the existence and uniqueness of an extremal quasiconformal mapping in a given homotopy class of mappings between Riemann surfaces, the theorems of Bers and Ahlfors on the completeness of Poincare theta series for general Fuchsian groups and the approximation of integrable holomorphic functions in a domain by rational functions with simple poles on the boundary of the domain. The modern aspects of the theory include Ahlfors's and Bers's natural complex analytic coordinates for Teichmuller space, the infinitesimal theory of Teichmuller's metric and Kobayashi's metric, Royden's theorem that the only biholomorphic self-mappings of Teichmuller's space are induced by elements of the modular group (the action of which group is discontinuous), the Hamilton-Krushkal necessary condition for extremality, and Reich and Strebel's proof of sufficiency.
Book Synopsis Foliations on Surfaces by : Igor Nikolaev
Download or read book Foliations on Surfaces written by Igor Nikolaev and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive, encyclopedic approach to the subject of foliations, one of the major concepts of modern geometry and topology. It addresses graduate students and researchers and serves as a reference book for experts in the field.
Book Synopsis On Quadratic Differentials and Extremal Quasiconformal Mappings by : Kurt Strebel
Download or read book On Quadratic Differentials and Extremal Quasiconformal Mappings written by Kurt Strebel and published by . This book was released on 1967 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariants of Quadratic Differential Forms by : Oswald Veblen
Download or read book Invariants of Quadratic Differential Forms written by Oswald Veblen and published by . This book was released on 1927 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: An early tract for students of differential geometry and mathematical physics.
Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos
Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
Book Synopsis Analysis Meets Geometry by : Mats Andersson
Download or read book Analysis Meets Geometry written by Mats Andersson and published by Birkhäuser. This book was released on 2017-09-04 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.
Book Synopsis A Gentle Introduction to Homological Mirror Symmetry by : Raf Bocklandt
Download or read book A Gentle Introduction to Homological Mirror Symmetry written by Raf Bocklandt and published by Cambridge University Press. This book was released on 2021-08-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to homological mirror symmetry from the point of view of representation theory, suitable for graduate students.
Book Synopsis Analysis and Mathematical Physics by : Björn Gustafsson
Download or read book Analysis and Mathematical Physics written by Björn Gustafsson and published by Springer Science & Business Media. This book was released on 2009-10-02 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
Book Synopsis Dictionary of Analysis, Calculus, and Differential Equations by : Douglas N. Clark
Download or read book Dictionary of Analysis, Calculus, and Differential Equations written by Douglas N. Clark and published by CRC Press. This book was released on 1999-12-15 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the occasional-if not frequent-need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Analysis, Calculus, and Differential Equations - the first published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,500 detailed definitions, written in a clear, readable style and complete with alternative meanings, and related references.
Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb
Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures 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 book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. 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.
Book Synopsis Univalent Functions and Conformal Mapping by : James A. Jenkins
Download or read book Univalent Functions and Conformal Mapping written by James A. Jenkins and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the application of the method of the extremal metric to the theory of univalent functions. Apart from an introductory chapter in which a brief survey of the development of this theory is given there is therefore no attempt to follow up other methods of treatment. Nevertheless such is the power of the present method that it is possible to include the great majority of known results on univalent functions. It should be mentioned also that the discussion of the method of the extremal metric is directed toward its application to univalent functions, there being no space to present its numerous other applications, particularly to questions of quasiconformal mapping. Also it should be said that there has been no attempt to provide an exhaustive biblio graphy, reference normally being confined to those sources actually quoted in the text. The central theme of our work is the General Coefficient Theorem which contains as special cases a great many of the known results on univalent functions. In a final chapter we give also a number of appli cations of the method of symmetrization. At the time of writing of this monograph the author has been re ceiving support from the National Science Foundation for which he wishes to express his gratitude. His thanks are due also to Sister BARBARA ANN Foos for the use of notes taken at the author's lectures in Geo metric Function Theory at the University of Notre Dame in 1955-1956.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author :American Mathematical Society Publisher :American Mathematical Soc. ISBN 13 :9780821801673 Total Pages :514 pages Book Rating :4.8/5 (16 download)
Book Synopsis Mathematics Into the Twenty-first Century by : American Mathematical Society
Download or read book Mathematics Into the Twenty-first Century written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 1992 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the summer of 1988 in Providence, the AMS celebrated its centennial with a wide range of mathematical activities. Among those was a symposium, Mathematics into the Twenty-first Century, which brought together a number of the top research mathematicians who will likely have a significant impact on the mathematics of this century. This book contains the lectures presented by 16 of the 18 individuals who spoke during the symposium. Written by some of the major international figures in mathematical research, this group of articles covers a panorama of the vital areas of mathematics at the turn of the 21st century and gives the general mathematical reader a broad perspective on some of the major trends in research.
Book Synopsis Differential Geometry and Complex Analysis by : I. Chavel
Download or read book Differential Geometry and Complex Analysis written by I. Chavel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and theta functions (ii) articles which would give the reader an idea of the depth and breadth of Rauch's researches, interests, and influence, in the fields he investigated, and (iii) articles of high scientific quality which would be of general interest. In each of the areas to which Rauch made significant contribution - pinching theorems, teichmiiller theory, and theta functions as they apply to Riemann surfaces - there has been substantial progress. Our hope is that the volume conveys the originality of Rauch's own work, the continuing vitality of the fields he influenced, and the enduring respect for, and tribute to, him and his accom plishments in the mathematical community. Finally, it is a pleasure to thank the Department of Mathematics, of the Grad uate School of the City University of New York, for their logistical support, James Rauch who helped us with the biography, and Springer-Verlag for all their efforts in producing this volume. Isaac Chavel . Hershel M. Farkas Contents Harry Ernest Rauch - Biographical Sketch. . . . . . . . VII Bibliography of the Publications of H. E. Rauch. . . . . . X Ph.D. Theses Written under the Supervision of H. E. Rauch. XIII H. E. Rauch, Geometre Differentiel (by M. Berger) . . . . . . . .
Book Synopsis Holomorphic Functions and Moduli I by : D. Drasin
Download or read book Holomorphic Functions and Moduli I written by D. Drasin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program.
Book Synopsis Geometric Complex Analysis - Proceedings Of The Third International Research Institute Of Mathematical Society Of Japan by : J Noguchi
Download or read book Geometric Complex Analysis - Proceedings Of The Third International Research Institute Of Mathematical Society Of Japan written by J Noguchi and published by World Scientific. This book was released on 1996-05-09 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is a collection of articles in several complex variables with emphasis on geometric methods and results, which includes several survey papers reviewing the development of the topics in these decades. Through this volume one can see an active field providing insight into other fields like algebraic geometry, dynamical systems and partial differential equations.
