Download or read book Proper Holomorphic Mappings in Several Complex Variables written by Marcus Wono Setya-Budhi and published by . This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: A holomorphic mapping f from a bounded domain D in $doubcsp{n}$ to a bounded domain $Omega$ in $doubcsp{N}$ is proper if the sequence ${f(zj)}$ tends to the boundary of $Omega$ for every sequence ${zj}$ which tends to the boundary of D. Let f be a proper holomorphic mapping from the unit ball in $doubcsp{n}$ to the unit ball in $doubcsp{N}$ for $N ge n ge 2.$ If f is a function of class $Csp{N-n+1}$ on the closed unit ball and also satisfies a certain non-degeneracy condition, then Cima and Suffridge proved that f must be rational. In this thesis we prove a similar result for mappings from complex eggs to the unit ball in $doubcsp{N}.$ We also prove that a rational proper holomorphic mapping f from the complex egg ${z in doubcsp{n} vertSigmavert zsb{i}

Download or read book Proper holomorphic mappings in several complex variables written by Franc Forstnerič and published by . This book was released on 1985 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first four chapters of this dissertation we study several problems concerning proper holomorphic mappings in several complex variables. In chapters 5 and 6 we study some questions on polynomial convexity.

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 Proper Holomorphic Mappings of Positive Codimension in Several Complex Variables written by Stephen Anthony Chiappari and published by . This book was released on 1990 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: A holomorphic mapping f from a bounded domain $Omega$ in C$sp{rm n}$ to a bounded domain $Omegaspprime$ in C$sp{rm N}$ is proper if and only if (f(z$sbnu$)) tends to the boundary b$Omegaspprime$ for each sequence (z$sbnu$) that tends to b$Omega$. If the domains are balls B$sb{rm n}$ and B$sb{rm N}$, Forstneric has proved that if f is sufficiently smooth up to the sphere bB$sb{rm n}$, then it must be rational, and Cima and Suffridge have shown that it then extends to be holomorphic past bB$sb{rm n}$. We prove the more general result that if (i) $Omega$ lies on one side of a real analytic real hypersurface M in C$sp{rm n}$, (ii) F maps $Omega$ holomorphically into the ball B$sb{rm N}$, (iii) in some neighborhood of a point p of M, F is the quotient of a holomorphic mapping by a holomorphic function, and (iv) if for each point q of M sufficiently near p, (F(z$sbnu$)) tends to bB$sb{rm N}$ as (z$sbnu$) tends to q within $Omega$, then F extends to be holomorphic past M at p. We prove this extension result also for certain other target domains, e.g., generalized ellipsoids $rm{sumsb{j} vert wsb{j}vertsp{2msb j}

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 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 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 Holomorphic Mappings and Algebras of Holomorphic Functions of Several Complex Variables written by Alan Trinler Huckleberry and published by . This book was released on 1970 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 319 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 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 Stein Manifolds and Holomorphic Mappings written by Franc Forstnerič and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.

Download or read book Several Complex Variables and Complex Geometry Part III written by Eric Bedford and published by American Mathematical Soc.. This book was released on 1991 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Function Theory in Several Complex Variables written by Carl H. FitzGerald and published by World Scientific. This book was released on 2004 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Download or read book Several Complex Variables written by KOHN and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been increasing interaction among various branches of mathematics. This is especially evident in the theory of several complex variables where fruitful interplays of the methods of algebraic geometry, differential geometry, and partial differential equations have led to unexpected insights and new directions of research. In China there has been a long tradition of study in complex analysis, differential geometry and differential equations as interrelated subjects due to the influence of Professors S. S. Chern and L. K. Hua. After a long period of isolation, in recent years there is a resurgence of scientific activity and a resumption of scientific exchange with other countries. The Hangzhou conference is the first international conference in several complex variables held in China. It offered a good opportunity for mathematicians from China, U.S., Germany, Japan, Canada, and France to meet and to discuss their work. The papers presented in the conference encompass all major aspects of several complex variables, in particular, in such areas as complex differential geometry, integral representation, boundary behavior of holomorphic functions, invariant metrics, holomorphic vector bundles, and pseudoconvexity. Most of the participants wrote up their talks for these proceedings. Some of the papers are surveys and the others present original results. This volume constitutes an overview of the current trends of research in several complex variables.

Download or read book Several Complex Variables and Complex Geometry Part I written by Eric Bedford and published by American Mathematical Soc.. This book was released on 1991 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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