Download or read book Entire Holomorphic Mappings in One and Several Complex Variables AM 85 Volume 85 written by Phillip A. Griffiths and published by Princeton University Press. This book was released on 2016-03-02 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974. In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order. Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the logarithmic derivative, R. Nevanlinna's proof of the defect relation, and refinements of the classical case.
Download or read book Entire Holomorphic Mappings in One and Several Complex Variables written by Phillip Griffiths and published by Princeton University Press. This book was released on 1976-02-21 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974. In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order. Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the logarithmic derivative, R. Nevanlinna's proof of the defect relation, and refinements of the classical case.
Download or read book Entire Functions of Several Complex Variables written by Pierre Lelong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Download or read book Equivalences of Holomorphic Mappings in One and Several Complex Variables written by Adrian Jenkins and published by . This book was released on 2005 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Theory of Analytic Functions of One or Several Complex Variables written by Henri Cartan and published by Courier Corporation. This book was released on 2013-04-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Download or read book Tasty Bits of Several Complex Variables written by Jiri Lebl and published by Lulu.com. This book was released on 2016-05-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
Download or read book Several Complex Variables and the Geometry of Real Hypersurfaces written by John P. D'Angelo and published by Routledge. This book was released on 2019-07-16 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.
Download or read book Several Complex Variables III written by G.M. Khenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
Download or read book Distribution of Values of Holomorphic Mappings written by Boris Vladimirovich Shabat and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A vast literature has grown up around the value distribution theory of meromorphic functions, synthesized by Rolf Nevanlinna in the 1920s and singled out by Hermann Weyl as one of the greatest mathematical achievements of this century. The multidimensional aspect, involving the distribution of inverse images of analytic sets under holomorphic mappings of complex manifolds, has not been fully treated in the literature. This volume thus provides a valuable introduction to multivariate value distribution theory and a survey of some of its results, rich in relations to both algebraic and differential geometry and surely one of the most important branches of the modern geometric theory of functions of a complex variable. Since the book begins with preparatory material from the contemporary geometric theory of functions, only a familiarity with the elements of multidimensional complex analysis is necessary background to understand the topic. After proving the two main theorems of value distribution theory, the author goes on to investigate further the theory of holomorphic curves and to provide generalizations and applications of the main theorems, focusing chiefly on the work of Soviet mathematicians.
Download or read book Introduction to Holomorphic Functions of Several Variables Volume I written by R.C. Gunning and published by Routledge. This book was released on 2018-05-02 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
Download or read book Introduction to Holomorphic Functions of Several Variables written by R.C. Gunning and published by CRC Press. This book was released on 1990-05-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
Download or read book Introduction to Holomorphic Functions of Several Variables Volume II written by R.C. Gunning and published by Routledge. This book was released on 2018-05-02 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
Download or read book Complex Analysis in one Variable written by NARASIMHAN and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a first-year graduate course I gave three times at the University of Chicago. As it was addressed to graduate students who intended to specialize in mathematics, I tried to put the classical theory of functions of a complex variable in context, presenting proofs and points of view which relate the subject to other branches of mathematics. Complex analysis in one variable is ideally suited to this attempt. Of course, the branches of mathema tics one chooses, and the connections one makes, must depend on personal taste and knowledge. My own leaning towards several complex variables will be apparent, especially in the notes at the end of the different chapters. The first three chapters deal largely with classical material which is avai lable in the many books on the subject. I have tried to present this material as efficiently as I could, and, even here, to show the relationship with other branches of mathematics. Chapter 4 contains a proof of Picard's theorem; the method of proof I have chosen has far-reaching generalizations in several complex variables and in differential geometry. The next two chapters deal with the Runge approximation theorem and its many applications. The presentation here has been strongly influenced by work on several complex variables.
Download or read book Hyperbolic Complex Spaces written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.
Download or read book Geometry of Holomorphic Mappings written by Sergey Pinchuk and published by Springer Nature. This book was released on 2023-10-16 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle. Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
Download or read book Function Theory of Several Complex Variables written by Steven George Krantz and published by American Mathematical Soc.. This book was released on 2001 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
