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Conformal Mapping Of Abstract Riemann Surfaces
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Book Synopsis Conformal Mapping on Riemann Surfaces by : Harvey Cohn
Download or read book Conformal Mapping on Riemann Surfaces written by Harvey Cohn and published by Courier Corporation. This book was released on 2014-05-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.
Book Synopsis Conformal Mapping of Abstract Riemann Surfaces by : Walter Helbig Gottschalk
Download or read book Conformal Mapping of Abstract Riemann Surfaces written by Walter Helbig Gottschalk and published by . This book was released on 1949 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Conformal Mapping of Simply-connected Riemann Surfaces. II by : Maurice Heins
Download or read book The Conformal Mapping of Simply-connected Riemann Surfaces. II written by Maurice Heins and published by . This book was released on 1957 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Riemann Surfaces by : Lars Valerian Ahlfors
Download or read book Riemann Surfaces written by Lars Valerian Ahlfors and published by Princeton University Press. This book was released on 2015-12-08 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30 by : Lars Valerian Ahlfors
Download or read book Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30 written by Lars Valerian Ahlfors and published by Princeton University Press. This book was released on 1953-08-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30, will be forthcoming.
Book Synopsis Conformal Mapping of Abstract Riemann Surfaces by : Walter Helbig Gottschalk
Download or read book Conformal Mapping of Abstract Riemann Surfaces written by Walter Helbig Gottschalk and published by . This book was released on 1949 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag
Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.
Book Synopsis Riemann Surfaces by : Lars Valerian Ahlfors
Download or read book Riemann Surfaces written by Lars Valerian Ahlfors and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.Originally published in 1960.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Classification Theory of Riemann Surfaces by : Leo Sario
Download or read book Classification Theory of Riemann Surfaces written by Leo Sario and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
Book Synopsis Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces by : Yunping Jiang
Download or read book Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces written by Yunping Jiang and published by American Mathematical Soc.. This book was released on 2012 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.
Book Synopsis Quasiconformal Mappings and Riemann Surfaces by : Samuil Leĭbovich Krushkalʹ
Download or read book Quasiconformal Mappings and Riemann Surfaces written by Samuil Leĭbovich Krushkalʹ and published by Winston Publishing. This book was released on 1979 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Maps Between Surfaces by : Jürgen Jost
Download or read book Harmonic Maps Between Surfaces written by Jürgen Jost and published by Springer. This book was released on 2006-12-08 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Extensions of Riemann Surfaces by : Tapani Jussila
Download or read book On Extensions of Riemann Surfaces written by Tapani Jussila and published by . This book was released on 1988 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Riemann Surfaces by : George Springer
Download or read book Introduction to Riemann Surfaces written by George Springer and published by Chelsea Publishing Company, Incorporated. This book was released on 1981 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text aims to introduce the reader to Riemann surfaces.
Book Synopsis Conformal Maps of a Riemannian Surface into the Space of Quaternions by : Dr. Jörg Richter
Download or read book Conformal Maps of a Riemannian Surface into the Space of Quaternions written by Dr. Jörg Richter and published by . This book was released on 1997-09-01 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present work, a coordinate-free way is suggested to handle conformal maps of a Riemannian surface into a space of constant curvature of maximum dimension 4, modeled on the non-commutative field of quaternions. This setup for the target space and the idea to treat differential 2-forms on Riemannian surfaces as quadratic functions on the tangent space, are the starting points for the development of the theory of conformal maps and in particular of conformal immersions. As a first result, very nice conditions for the conformality of immersions into 3- and 4-dimensional space-forms are deduced and a simple way to write the second fundamental form is found. If the target space is euclidean 3-space, an alternative approach is proposed by fixing a spin structure on the Riemannian surface. The problem of finding a local immersion is then reduced to that of solving a linear Dirac equation with a potential whose square is the Willmore integrand. This allows to make statements about the structure of the moduli space of conformal immersions and to derive a very nice criterion for a conformal immersion to be constrained Willmore. As an application the Dirac equation with constant potential over spheres and tori is solved. This yields explicit immersion formulae out of which there were produced pictures, the Dirac-spheres and -tori. These immersions have the property that their Willmore integrand generates a metric of vanishing and constant curvature, respectively. As a next step an affine immersion theory is developped. This means, one starts with a given conformal immersion into euclidean 3-space and looks for new ones in the same conformal class. This is called a spin-transformation and it leads one to solve an affine Dirac equation. Also, it is shown how the coordinate-dependent generalized Weierstrass representation fits into the present framework. In particular, it is now natural to consider the class of conformal immersions that admit new conformal immersions having the same potential. It turns out, that all geometrically interesting immersions admit such an isopotential spin-transformation and that this property of an immersion is even a conformal invariant of the ambient space. It is shown that conformal isothermal immersions generate both via their dual and via Darboux transformations non-trivial families of new isopotential conformal immersions. Similarly to this, conformal (constrained) Willmore immersions produce non-trivial families of isopotential immersions of which subfamilies are (constrained) Willmore again having even the same Willmore integral. Another observation is, that the Euler-Lagrange equation for the Willmore problem is the integrability condition for a quaternionic 1-form, which generates a conformal minimal immersions into hyperbolic 4-space. Vice versa, any such immersion determines a conformal Willmore immersion. As a consequence, there is a one-to-one correspondence between conformal minimal immersions into Lorentzian space and those into hyperbolic space, which generalizes to any dimension. There is also induced an action on conformal minimal immersions into hyperbolic 4-space. Another fact is, that conformal constant mean curvature (cmc) immersions into some 3-dimensional space form unveil to be isothermal and constrained Willmore. The reverse statement is true at least for tori. Finally a very simple proof of a theorem by R.Bryant concerning Willmore spheres is given. In the last part, time-dependent conformal immersions are considered. Their deformation formulae are computed and it is investigated under what conditions the flow commutes with Moebius transformations. The modified Novikov-Veselov flow is written down in a conformal invariant way and explicit deformation formulae for the immersion function itself and all of its invariants are given. This flow commutes with Moebius transformations. Its definition is coupled with a delta-bar problem, for which a solution is presented under special conditions. These are fulfilled at least by cmc immersions and by surfaces of revolution and the general flow formulae reduce to very nice formulae in these cases.
Book Synopsis Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces by : R. Courant
Download or read book Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces written by R. Courant and published by Springer. This book was released on 1977-06-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance. The present book deals with subjects of this category. It is written in a style which, as the author hopes, expresses adequately the balance and tension between the individuality of mathematical objects and the generality of mathematical methods. The author has been interested in Dirichlet's Principle and its various applications since his days as a student under David Hilbert. Plans for writing a book on these topics were revived when Jesse Douglas' work suggested to him a close connection between Dirichlet's Principle and basic problems concerning minimal sur faces. But war work and other duties intervened; even now, after much delay, the book appears in a much less polished and complete form than the author would have liked.
Book Synopsis Functionals of Finite Riemann Surfaces by : Menahem Schiffer
Download or read book Functionals of Finite Riemann Surfaces written by Menahem Schiffer and published by Courier Corporation. This book was released on 2014-06-01 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph on finite Riemann surfaces, based on the authors' 1949–50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of "a plethora of ideas, each interesting in its own right," noting that "the patient reader will be richly rewarded." Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theorems for finite Riemann surfaces, and relations between differentials. Subsequent chapters explore bilinear differentials, surfaces imbedded in a given surface, integral operators, and variations of surfaces and of their functionals. The book concludes with a look at applications of the variational method and remarks on generalization to higher dimensional Kahler manifolds.
