Topics in the Theory of Riemann Surfaces, Robert D.M. Accola

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: Khovanskii, Askold
Название: Galois theory, coverings, and riemann surfaces
ISBN: 364238840X ISBN-13(EAN): 9783642388408
Издательство: Springer
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Описание: Galois Theory, Coverings, and Riemann Surfaces

Автор: Y. Rodin
Название: The Riemann Boundary Problem on Riemann Surfaces
ISBN: 9027726531 ISBN-13(EAN): 9789027726537
Издательство: Springer
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Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Автор: Leo Sario; Mitsuru Nakai
Название: Classification Theory of Riemann Surfaces
ISBN: 3642482716 ISBN-13(EAN): 9783642482717
Издательство: Springer
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Описание: 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.

Автор: Christian Klein; Olaf Richter
Название: Ernst Equation and Riemann Surfaces
ISBN: 3642066771 ISBN-13(EAN): 9783642066771
Издательство: Springer
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Цена: 11099.00 р.
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Описание: Exact solutions to Einstein`s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory.

Автор: Hershel M. Farkas; Irwin Kra
Название: Riemann Surfaces
ISBN: 1461273919 ISBN-13(EAN): 9781461273912
Издательство: Springer
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Цена: 9781.00 р.
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Описание: This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel`s theorem, the Jacobi inversion problem, Noether`s theorem, and the Riemann vanishing theorem.