The Riemann Boundary Problem on Riemann Surfaces, Y. Rodin

Автор: Bobenko
Название: Computational Approach to Riemann Surfaces
ISBN: 3642174124 ISBN-13(EAN): 9783642174124
Издательство: Springer
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Описание: 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.

Автор: Gunning Robert C.
Название: Lectures on Riemann Surfaces: Jacobi Varieties
ISBN: 0691619255 ISBN-13(EAN): 9780691619255
Издательство: Wiley
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Описание: 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 pres

Автор: I.V. Ostrovskii; I.V. Ostrovskii; Yu.I. Lyubarskii
Название: Riemann`s Boundary Problem with Infinite Index
ISBN: 3034896557 ISBN-13(EAN): 9783034896559
Издательство: Springer
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Описание: PREFACE The classic statement of the Riemann boundary problem consists in finding a function (z) which is analytic and bounded in two domains D+ and D-, with a common boundary - a smooth closed contour L admitting a continuous extension onto L both from D+ and D- and satisfying on L the boundary condition +(t) = G(t)-(t) + g(t).

Автор: Bruce Gilligan; Otto Forster
Название: Lectures on Riemann Surfaces
ISBN: 0387906177 ISBN-13(EAN): 9780387906171
Издательство: Springer
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Описание: Based on the lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Munster, this book provides a modern introduction to this subject, presenting methods used in the study of complex manifolds in the special case of complex dimension one.

Автор: I.V. Ostrovskii; I.V. Ostrovskii; Yu.I. Lyubarskii
Название: Riemann`s Boundary Problem with Infinite Index
ISBN: 3764329998 ISBN-13(EAN): 9783764329990
Издательство: Springer
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Описание: PREFACE The classic statement of the Riemann boundary problem consists in finding a function (z) which is analytic and bounded in two domains D+ and D-, with a common boundary - a smooth closed contour L admitting a continuous extension onto L both from D+ and D- and satisfying on L the boundary condition +(t) = G(t)-(t) + g(t).

Автор: Jones, Gareth A., Wolfart, J?rgen
Название: Dessins d`Enfants on Riemann Surfaces
ISBN: 3319247093 ISBN-13(EAN): 9783319247090
Издательство: Springer
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Описание: This volume provides an introduction to dessins d`enfants and embeddings of bipartite graphs in compact Riemann surfaces.

Автор: Andrei Bogatyrev; Nikolai Kruzhilin
Название: Extremal Polynomials and Riemann Surfaces
ISBN: 364244332X ISBN-13(EAN): 9783642443329
Издательство: Springer
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Описание: This book develops the classical Chebyshev`s approach which gives analytical representation for the solution in terms of Riemann surfaces. It includes numerous problems, exercises, and illustrations.