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Author : Robert J. Sibner
Publisher : Unknown
Page : 34 pages
File Size : 44,9 Mb
Release : 1964
Category : Riemann surfaces
ISBN : UOM:39015017417125
Author : Emilio Bujalance,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer
Page : 164 pages
File Size : 44,5 Mb
Release : 2010-09-29
Category : Mathematics
ISBN : 9783642148286
This monograph covers symmetries of compact Riemann surfaces. It examines the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Author : Samuil Leĭbovich Krushkalʹ,Boris Nikolaevich Apanasov,Nikolaĭ Aleksandrovich Gusevskiĭ
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 55,7 Mb
Release : 1986
Category : Kleinian groups
ISBN : 9780821845165
Presents a unified exposition of the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. This book lists the basic facts regarding Kleinian groups and serves as a general guide to the primary literature, particularly the Russian literature in the field.
Author : Lars Valerian Ahlfors
Publisher : Princeton University Press
Page : 436 pages
File Size : 43,8 Mb
Release : 1971-07-21
Category : Mathematics
ISBN : 069108081X
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.
Author : Leon Greenberg
Publisher : Princeton University Press
Page : 452 pages
File Size : 55,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881642
Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.
Author : Clifford J. Earle,William J. Harvey,Sevín Recillas-Pishmish
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 54,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829578
This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results, and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning Riemann surfaces, as well as a wide scope of other issues: the theory of Teichmuller spaces, theta functions, algebraic geometry and classical function theory. Included here are discussions revolving around questions of geometry that are related in one way or another to functions of a complex variable. There are contributors on Riemann surfaces, hyperbolic geometry, Teichmuller spaces, and quasiconformal maps. Complex geometry has many applications--triangulations of surfaces, combinatorics, ordinary differential equations, complex dynamics, and the geometry of special curves and jacobians, among others. In this book, research mathematicians in complex geometry, hyperbolic geometry and Teichmuller spaces will find a selection of strong papers by international experts.
Author : Alexander I. Bobenko
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 53,6 Mb
Release : 2011-02-12
Category : Mathematics
ISBN : 9783642174124
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
Author : Robert M. Guralnick,John Shareshian
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 52,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839928
The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X \rightarrow \mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g \ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small.
Author : Anonim
Publisher : Unknown
Page : 580 pages
File Size : 43,8 Mb
Release : 1965
Category : Mathematics
ISBN : UCAL:B3632410
Author : Lars Valerian Ahlfors,Leo Sario
Publisher : Princeton University Press
Page : 397 pages
File Size : 43,6 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400874538
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.
Author : Francis E. Burstall,John H. Rawnsley
Publisher : Springer
Page : 120 pages
File Size : 54,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470526
In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.
Author : Lars Valerian Ahlfors,E. Calabi,Marston Morse,Leo Sario,Donald Clayton Spencer
Publisher : Princeton University Press
Page : 275 pages
File Size : 45,7 Mb
Release : 1953-08-21
Category : Mathematics
ISBN : 9780691079394
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author : Robert C. Gunning
Publisher : Princeton University Press
Page : 198 pages
File Size : 55,8 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400872695
A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well. The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. 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.
Author : Robert D.M. Accola
Publisher : Springer
Page : 117 pages
File Size : 43,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540490562
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 2007
Category : Electronic
ISBN : OCLC:207734169