Описание: The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.
Автор: Bergeron, Nicolas Название: Spectrum of hyperbolic surfaces ISBN: 3319276646 ISBN-13(EAN): 9783319276649 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called "arithmetic hyperbolic surfaces", the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them.
After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss.
The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Автор: David Mond, Juan Jos? Nu?o-Ballesteros Название: Singularities of Mappings ISBN: 3030344398 ISBN-13(EAN): 9783030344399 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Поставка под заказ.
Описание: The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C and complex analytic theories jointly.
Автор: Franc Forstneri? Название: Stein Manifolds and Holomorphic Mappings ISBN: 3319610570 ISBN-13(EAN): 9783319610573 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The theme of this book is an examination of the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds, offering the first complete account of Oka-Grauert theory and its modern extensions.
Автор: Stanislav Hencl; Pekka Koskela Название: Lectures on Mappings of Finite Distortion ISBN: 3319031724 ISBN-13(EAN): 9783319031729 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion.
Автор: Pei-Chu Hu; Ping Li; Chung-Chun Yang Название: Unicity of Meromorphic Mappings ISBN: 1441952438 ISBN-13(EAN): 9781441952431 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.
Описание: Extending Griffiths` classical theory of period mappings for compact Kahler manifolds, this book develops and applies a theory of period mappings of "Hodge-de Rham type" for families of open complex manifolds.
Автор: Hariri Parisa, Klйn Riku, Vuorinen Matti Название: Conformally Invariant Metrics and Quasiconformal Mappings ISBN: 3030320677 ISBN-13(EAN): 9783030320676 Издательство: Springer Цена: 16769.00 р. Наличие на складе: Поставка под заказ.
Описание: This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). The authors` approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book.
Автор: Borthwick Название: Spectral Theory of Infinite-Area Hyperbolic Surfaces ISBN: 3319338757 ISBN-13(EAN): 9783319338750 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution.The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition:'The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it.' (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)
Описание: This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappi
Автор: Franc Forstneri? Название: Stein Manifolds and Holomorphic Mappings ISBN: 3319869949 ISBN-13(EAN): 9783319869940 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Поставка под заказ.
Описание: The theme of this book is an examination of the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds, offering the first complete account of Oka-Grauert theory and its modern extensions.
Автор: Peter Duren; Juha Heinonen; Brad Osgood; Bruce Pal Название: Quasiconformal Mappings and Analysis ISBN: 038798299X ISBN-13(EAN): 9780387982991 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers a selection of expository articles that were written in conjunction with an international conference held to honor FW Gehring on the occasion of his 70th birthday. This book aims to survey various topics related to Gehring`s fundamental research in the field of quasiconformal mappings.
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