Riemann Surfaces Of Infinite Genus
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Riemann Surfaces Of Infinite Genus
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Author : Joel S. Feldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Riemann Surfaces Of Infinite Genus written by Joel S. Feldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Riemann surfaces categories.
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.
Integrable Systems And Riemann Surfaces Of Infinite Genus
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Author : Martin Ulrich Schmidt
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Integrable Systems And Riemann Surfaces Of Infinite Genus written by Martin Ulrich Schmidt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This memoir develops the spectral theory of the Lax operators of nonlinear Schrodinger-like partial differential equations with periodic boundary conditions. Their spectral curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces. In fact, some of the basic tools of the theory of compact Riemann surfaces are generalized to these spectral curves and illuminate the structure of complete integrability: The eigen bundles define holomorphic line bundles on the spectral curves, which completely determine the potentials. These line bundles may be described by divisors of the same degree as the genus, and these divisors give rise to Darboux coordinates. With the help of a Riemann-Roch Theorem, the isospectral sets (the sets of all potentials corresponding to the same spectral curve) may be identified with open dense subsets of the Jacobian varieties. The real parts of the isospectral sets are infinite dimensional tori, and the group action solves the corresponding nonlinear partial differential equations. Deformations of the spectral curves are in one to one correspondence with holomorphic forms. Serre Duality reproduces the symplectic form.
Topics In The Theory Of Riemann Surfaces
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Author : Robert D.M. Accola
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Theory Of Riemann Surfaces written by Robert D.M. Accola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Contributions To The Theory Of Riemann Surfaces
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Author : Lars Valerian Ahlfors
language : en
Publisher: Princeton University Press
Release Date : 1953-08-21
Contributions To The Theory Of Riemann Surfaces written by Lars Valerian Ahlfors and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953-08-21 with Mathematics categories.
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.
Riemann Surfaces And Generalized Theta Functions
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Author : Robert C. Gunning
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Riemann Surfaces And Generalized Theta Functions written by Robert C. Gunning and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.
Riemann Surfaces Theta Functions And Abelian Automorphisms Groups
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Author : R.D.M. Accola
language : en
Publisher: Springer
Release Date : 2006-11-14
Riemann Surfaces Theta Functions And Abelian Automorphisms Groups written by R.D.M. Accola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Compact Riemann Surfaces
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Author : R. Narasimhan
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Compact Riemann Surfaces written by R. Narasimhan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Compact Riemann Surfaces
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Compact Riemann Surfaces written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Symmetries Of Compact Riemann Surfaces
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Author : Emilio Bujalance
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-06
Symmetries Of Compact Riemann Surfaces written by Emilio Bujalance and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-06 with Mathematics categories.
This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Discontinuous Groups And Riemann Surfaces Am 79 Volume 79
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Author : Leon Greenberg
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Discontinuous Groups And Riemann Surfaces Am 79 Volume 79 written by Leon Greenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
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.