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    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint

    Posted By: AvaxGenius
    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint

    Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint by Gregor Fels , Alan Huckleberry , Joseph A. Wolf
    English | PDF (True) | 2006 | 342 Pages | ISBN : 0817643915 | 2.8 MB

    This research monograph is a systematic exposition of the background, methods, and recent results in the theory of cycle spaces of ?ag domains. Some of the methods are now standard, but many are new. The exposition is carried out from the viewpoint of complex algebraic and differential geometry. Except for certain foundational material,whichisreadilyavailablefromstandardtexts,itisessentiallyself-contained; at points where this is not the case we give extensive references. After developing the background material on complex ?ag manifolds and rep- sentationtheory, wegiveanexposition(withanumberofnewresults)ofthecomplex geometric methods that lead to our characterizations of (group theoretically de?ned) cycle spaces and to a number of consequences.

    Theory of Stein Spaces

    Posted By: AvaxGenius
    Theory of Stein Spaces

    Theory of Stein Spaces by Hans Grauert , Reinhold Remmert
    English | PDF (True) | 2004 | 273 Pages | ISBN : 3540003738 | 28.5 MB

    "Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book."

    Rigid Analytic Geometry and Its Applications

    Posted By: AvaxGenius
    Rigid Analytic Geometry and Its Applications

    Rigid Analytic Geometry and Its Applications by Jean Fresnel , Marius Put
    English | PDF (True) | 303 Pages | ISBN : 0817642064 | 32.7 MB

    Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.

    An Introduction to the Kähler-Ricci Flow

    Posted By: AvaxGenius
    An Introduction to the Kähler-Ricci Flow

    An Introduction to the Kähler-Ricci Flow by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj
    English | PDF (True) | 2013 | 342 Pages | ISBN : 3319008188 | 2.8 MB

    This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research.

    Handbook of Complex Variables

    Posted By: AvaxGenius
    Handbook of Complex Variables

    Handbook of Complex Variables by Steven G. Krantz
    English | PDF | 1999 | 301 Pages | ISBN : 0817640118 | 17.8 MB

    This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica­ tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground­ ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com­ pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.

    Complex Variables with Applications

    Posted By: AvaxGenius
    Complex Variables with Applications

    Complex Variables with Applications by S. Ponnusamy , Herb Silverman
    English | PDF (True) | 2006 | 521 Pages | ISBN : 0817644571 | 4.6 MB

    Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics.

    Computational Methods for Linear Integral Equations

    Posted By: AvaxGenius
    Computational Methods for Linear Integral Equations

    Computational Methods for Linear Integral Equations by Prem K. Kythe , Pratap Puri
    English | PDF (True) | 2002 | 525 Pages | ISBN : 0817641920 | 30.8 MB

    This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover­ ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag­ netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys­ tems, communication theory, mathematical economics, population genetics, queue­ ing theory, and medicine. Most of the boundary value problems involving differ­ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

    The Bergman Kernel and Related Topics

    Posted By: AvaxGenius
    The Bergman Kernel and Related Topics

    The Bergman Kernel and Related Topics: Hayama Symposium on SCV XXIII, Kanagawa, Japan, July 2022 by Kengo Hirachi, Takeo Ohsawa, Shigeharu Takayama, Joe Kamimoto
    English | PDF EPUB (True) | 2024 | 372 Pages | ISBN : 9819995051 | 51 MB

    This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel. The symposium took place in Hayama and Tokyo in July 2022. Each article is closely related to the Bergman kernel, covering topics in complex analysis, differential geometry, representation theory, PDE, operator theory, and complex algebraic geometry.

    From Holomorphic Functions to Complex Manifolds

    Posted By: AvaxGenius
    From Holomorphic Functions to Complex Manifolds

    From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche , Hans Grauert
    English | PDF (True) | 2002 | 406 Pages | ISBN : 0387953957 | 32.1 MB

    The aim of this book is to give an understandable introduction to the the­ ory of complex manifolds. With very few exceptions we give complete proofs. Many examples and figures along with quite a few exercises are included. Our intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involved with sheaves, coherence, and higher-dimensional cohomology are avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional co­ cycles are used.

    Complex Spaces in Finsler, Lagrange and Hamilton Geometries

    Posted By: AvaxGenius
    Complex Spaces in Finsler, Lagrange and Hamilton Geometries

    Complex Spaces in Finsler, Lagrange and Hamilton Geometries by Gheorghe Munteanu
    English | PDF | 2004 | 237 Pages | ISBN : 1402022050 | 18.5 MB

    From a historical point of view, the theory we submit to the present study has its origins in the famous dissertation of P. Finsler from 1918 ([Fi]). In a the classical notion also conventional classification, Finsler geometry has besides a number of generalizations, which use the same work technique and which can be considered self-geometries: Lagrange and Hamilton spaces. Finsler geometry had a period of incubation long enough, so that few math­ ematicians (E. Cartan, L. Berwald, S.S. Chem, H. Rund) had the patience to penetrate into a universe of tensors, which made them compare it to a jungle. To aU of us, who study nowadays Finsler geometry, it is obvious that the qualitative leap was made in the 1970's by the crystallization of the nonlinear connection notion (a notion which is almost as old as Finsler space, [SZ4]) and by work-skills into its adapted frame fields. The results obtained by M. Matsumoto (coUected later, in 1986, in a monograph, [Ma3]) aroused interest not only in Japan, but also in other countries such as Romania, Hungary, Canada and the USA, where schools of Finsler geometry are founded and are presently widely recognized.

    Value Distribution Theory and Related Topics

    Posted By: AvaxGenius
    Value Distribution Theory and Related Topics

    Value Distribution Theory and Related Topics by G. Barsegian, I. Laine, C. C. Yang
    English | PDF (True) | 2004 | 331 Pages | ISBN : 1402079508 | 34.1 MB

    The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

    Resolution of Curve and Surface Singularities in Characteristic Zero

    Posted By: AvaxGenius
    Resolution of Curve and Surface Singularities in Characteristic Zero

    Resolution of Curve and Surface Singularities in Characteristic Zero by K. Kiyek , J. L. Vicente
    English | PDF | 2004 | 506 Pages | ISBN : 1402020287 | 50.3 MB

    The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans­ formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

    Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses (Repost)

    Posted By: AvaxGenius
    Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses (Repost)

    Calabi-Yau Varieties: Arithmetic, Geometry and Physics: Lecture Notes on Concentrated Graduate Courses by Radu Laza, Matthias Schütt, Noriko Yui
    English | EPUB | 2015 | 548 Pages | ISBN : 1493928295 | 7.7 MB

    This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area.

    Multidimensional Integral Representations: Problems of Analytic Continuation (Repost)

    Posted By: AvaxGenius
    Multidimensional Integral Representations: Problems of Analytic Continuation (Repost)

    Multidimensional Integral Representations: Problems of Analytic Continuation by Alexander M. Kytmanov, Simona G. Myslivets
    English | EPUB | 2015 | 225 Pages | ISBN : 3319216589 | 3.7 MB

    The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem.