Holomorphic Curves and Global Questions in Contact Geometry, Casim Abbas; Helmut Hofer

Автор: Chris Wendl
Название: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
ISBN: 1108497403 ISBN-13(EAN): 9781108497404
Издательство: Cambridge Academ
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Цена: 121440.00 T
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Описание: Based on a series of lectures for students in topology, this book provides an entry point into the intersection theory of punctured holomorphic curves. Appendices featuring quick reference guides for applying the theory and self-contained proofs of key technical results also make it a valuable resource for researchers.

Автор: Carlo Gasbarri, Steven Lu, Mike Roth, Yuri Tschinkel
Название: Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties
ISBN: 1470414589 ISBN-13(EAN): 9781470414580
Издательство: Mare Nostrum (Eurospan)
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Цена: 104410.00 T
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Описание: Contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held in June 2013. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties.

Автор: Michele Audin; Jacques Lafontaine
Название: Holomorphic Curves in Symplectic Geometry
ISBN: 3034896565 ISBN-13(EAN): 9783034896566
Издательство: Springer
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Цена: 46570.00 T
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Автор: Roelof Bruggeman, Youngju Choie, Nikolaos Diamantis
Название: Holomorphic Automorphic Forms and Cohomology
ISBN: 1470428555 ISBN-13(EAN): 9781470428556
Издательство: Mare Nostrum (Eurospan)
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Цена: 77610.00 T
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Описание: Investigates the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least $2$ this correspondence is given by the Eichler integral. The authors use Knopp`s generalization of this integral to real weights, and apply it to complex weights that are not an integer at least $2$.

Автор: Urs Frauenfelder; Otto van Koert
Название: The Restricted Three-Body Problem and Holomorphic Curves
ISBN: 3030101800 ISBN-13(EAN): 9783030101800
Издательство: Springer
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Цена: 102480.00 T
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Описание: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.This book is also part of the Virtual Series on Symplectic Geometryhttp://www.springer.com/series/16019

Автор: Christoph Hummel
Название: Gromov`s Compactness Theorem for Pseudo-holomorphic Curves
ISBN: 3034898428 ISBN-13(EAN): 9783034898423
Издательство: Springer
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Цена: 46570.00 T
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Описание: This book presents the original proof of Gromov`s compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint.

Автор: Wendl
Название: Holomorphic Curves in Low Dimensions
ISBN: 3319913697 ISBN-13(EAN): 9783319913698
Издательство: Springer
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Цена: 55890.00 T
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Описание: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds.This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

Автор: Frauenfelder
Название: The Restricted Three-Body Problem and Holomorphic Curves
ISBN: 3319722778 ISBN-13(EAN): 9783319722771
Издательство: Springer
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Цена: 111790.00 T
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Описание:

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics.

The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.

Автор: D. Drasin; C.J. Earle; F.W. Gehring; I. Kra; A. Ma
Название: Holomorphic Functions and Moduli I
ISBN: 1461396042 ISBN-13(EAN): 9781461396048
Издательство: Springer
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Цена: 111790.00 T
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Описание: The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe- maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution.

Автор: Mark Elin; Simeon Reich; David Shoikhet
Название: Numerical Range of Holomorphic Mappings and Applications
ISBN: 303005019X ISBN-13(EAN): 9783030050191
Издательство: Springer
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Цена: 79190.00 T
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Описание: This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.

Автор: Franc Forstneri?
Название: Stein Manifolds and Holomorphic Mappings
ISBN: 3319610570 ISBN-13(EAN): 9783319610573
Издательство: Springer
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Цена: 121110.00 T
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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: R. Michael Range
Название: Holomorphic Functions and Integral Representations in Several Complex Variables
ISBN: 1441930787 ISBN-13(EAN): 9781441930781
Издательство: Springer
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Цена: 68900.00 T
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Описание: The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu- lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ- ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com- plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.