Bounded Holomorphic Functions on Finite Riemann Surfaces PDF Download
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Author: Edgar Lee Stout
Publisher:
ISBN:
Category : Holomorphic functions
Languages : en
Pages : 172
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Book Description
Author: Edgar Lee Stout
Publisher:
ISBN:
Category : Holomorphic functions
Languages : en
Pages : 172
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Book Description
Author: Wilhelm Schlag
Publisher: American Mathematical Society
ISBN: 0821898477
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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.
Author: Joel S. Feldman
Publisher: American Mathematical Soc.
ISBN: 082183357X
Category : Mathematics
Languages : en
Pages : 306
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Book Description
In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps. The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of Kadomcev-Petviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces). The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.
Author: Roy Wyatt Pengra
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
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Book Description
Author: Marco Abate
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110601974
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.
Author: Benson Farb
Publisher: American Mathematical Soc.
ISBN: 0821898876
Category : Mathematics
Languages : en
Pages : 371
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Book Description
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.
Author: M. Hasumi
Publisher: Springer
ISBN: 3540387196
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Author: Stephen D. Fisher
Publisher: Courier Corporation
ISBN: 0486151107
Category : Mathematics
Languages : en
Pages : 292
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Book Description
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
Author: Henri Paul de Saint-Gervais
Publisher:
ISBN: 9783037191453
Category : Curves, Algebraic
Languages : en
Pages : 0
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Book Description
In 1907, Paul Koebe and Henri Poincare almost simultaneously proved the uniformization theorem: Every simply connected Riemann surface is isomorphic to the plane, the open unit disc, or the sphere. It took a whole century to get to the point of stating this theorem and providing a convincing proof of it, relying as it did on prior work of Gauss, Riemann, Schwarz, Klein, Poincare, and Koebe, among others. The present book offers an overview of the maturation process of this theorem. The evolution of the uniformization theorem took place in parallel with the emergence of modern algebraic geometry, the creation of complex analysis, the first stirrings of functional analysis, and with the flowering of the theory of differential equations and the birth of topology. The uniformization theorem was, thus, one of the lightning rods of 19th century mathematics. Rather than describe the history of a single theorem, the book aims to return to the original proofs, to look at these through the eyes of modern mathematicians, to inquire as to their correctness, and to attempt to make them rigorous while respecting, as much as possible, the state of mathematical knowledge at the time, or, if this should prove impossible, then to use modern mathematical tools that were not available to the authors of the original proofs. This book will be useful to mathematicians wishing to cast a glance back at the history of their discipline. It should also provide graduate students with a non-standard approach to concepts of great importance for modern research.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 256
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Book Description
