The Geometry Of Complex Domains

Author : Robert E. Greene,Kang-Tae Kim,Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 46,9 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9780817646226

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The Geometry of Complex Domains by Robert E. Greene,Kang-Tae Kim,Steven G. Krantz Pdf

This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.

Author : Julian Lowell Coolidge
Publisher : Unknown
Page : 252 pages
File Size : 42,9 Mb
Release : 1924
Category : Collineation
ISBN : WISC:89062907332

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The Geometry of the Complex Domain by Julian Lowell Coolidge Pdf

Author : Jacques Faraut,Soji Kaneyuki,Adam Koranyi,Qi-keng Lu,Guy Roos
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213666

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Analysis and Geometry on Complex Homogeneous Domains by Jacques Faraut,Soji Kaneyuki,Adam Koranyi,Qi-keng Lu,Guy Roos Pdf

A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.

Author : JULIAN LOWELL. COOLIDGE
Publisher : Unknown
Page : 0 pages
File Size : 48,7 Mb
Release : 2018
Category : Electronic
ISBN : 1033363057

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GEOMETRY OF THE COMPLEX DOMAIN by JULIAN LOWELL. COOLIDGE Pdf

Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215745

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The Geometry of Domains in Space by Steven G. Krantz,Harold R. Parks Pdf

The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.

Author : Jacques Faraut,Soji Kaneyuki,Adam Koranyi
Publisher : Unknown
Page : 560 pages
File Size : 43,6 Mb
Release : 1999-12-10
Category : Electronic
ISBN : 1461213673

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Analysis and Geometry on Complex Homogeneous Domains by Jacques Faraut,Soji Kaneyuki,Adam Koranyi Pdf

Author : Simeon Reich,David Shoiykhet
Publisher : Imperial College Press
Page : 372 pages
File Size : 47,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860947148

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Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces by Simeon Reich,David Shoiykhet Pdf

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces. Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments. Contents: Mappings in Metric and Normed Spaces; Differentiable and Holomorphic Mappings in Banach Spaces; Hyperbolic Metrics on Domains in Complex Banach Spaces; Some Fixed Point Principles; The DenjoyOCoWolff Fixed Point Theory; Generation Theory for One-Parameter Semigroups; Flow-Invariance Conditions; Stationary Points of Continuous Semigroups; Asymptotic Behavior of Continuous Flows; Geometry of Domains in Banach Spaces."

Author : Gregor Fels,Alan Huckleberry,Joseph A. Wolf
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 45,9 Mb
Release : 2005-12-12
Category : Mathematics
ISBN : 0817643915

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Cycle Spaces of Flag Domains by Gregor Fels,Alan Huckleberry,Joseph A. Wolf Pdf

Driven by numerous examples from the complex geometric viewpoint New results presented for the first time Widely accessible, with all necessary background material provided for the nonspecialist Comparisons with classical Barlet cycle spaces are given Good bibliography and index

Author : Dominique Cerveau
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 45,7 Mb
Release : 2003
Category : Mathematics
ISBN : 082183228X

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Complex Dynamics and Geometry by Dominique Cerveau Pdf

In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.

Author : John P. D'Angelo
Publisher : Routledge
Page : 319 pages
File Size : 47,5 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416719

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Several Complex Variables and the Geometry of Real Hypersurfaces by John P. D'Angelo Pdf

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Author : Mark Green,Phillip A. Griffiths,Matt Kerr
Publisher : Princeton University Press
Page : 298 pages
File Size : 40,7 Mb
Release : 2012-04-22
Category : Mathematics
ISBN : 9781400842735

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Mumford-Tate Groups and Domains by Mark Green,Phillip A. Griffiths,Matt Kerr Pdf

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 42,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814918

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Several Complex Variables and Complex Geometry, Part III by Eric Bedford Pdf

Author : E. Vesentini
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 52,6 Mb
Release : 2011-06-08
Category : Mathematics
ISBN : 9783642110603

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Geometry of Homogeneous Bounded Domains by E. Vesentini Pdf

S.G. Gindikin, I.I. Pjateckii-Sapiro, E.B. Vinberg: Homogeneous Kähler manifolds.- S.G. Greenfield: Extendibility properties of real submanifolds of Cn.- W. Kaup: Holomorphische Abbildungen in Hyperbolische Räume.- A. Koranyi: Holomorphic and harmonic functions on bounded symmetric domains.- J.L. Koszul: Formes harmoniques vectorielles sur les espaces localement symétriques.- S. Murakami: Plongements holomorphes de domaines symétriques.- E.M. Stein: The analogues of Fatous’s theorem and estimates for maximal functions.

Author : Oswald Veblen
Publisher : Unknown
Page : 542 pages
File Size : 46,7 Mb
Release : 1937
Category : Complexes
ISBN : UOM:39015011426999

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Geometry of Complex Domains by Oswald Veblen Pdf

Author : Gregor Fels,Alan Huckleberry,Joseph A. Wolf
Publisher : Birkhäuser
Page : 339 pages
File Size : 45,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0817671005

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Cycle Spaces of Flag Domains by Gregor Fels,Alan Huckleberry,Joseph A. Wolf Pdf

Driven by numerous examples from the complex geometric viewpoint New results presented for the first time Widely accessible, with all necessary background material provided for the nonspecialist Comparisons with classical Barlet cycle spaces are given Good bibliography and index