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 Proper Holomorphic Mappings written by Victoria Pambuccian and published by . This book was released on 1994 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proper holomorphic mappings A survey written by Franc Forstnerič and published by . This book was released on 1991 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Stein Manifolds and Holomorphic Mappings written by Franc Forstnerič and published by Springer. This book was released on 2017-09-05 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
Download or read book PROPER HOLOMORPHIC MAPPINGS IN DOUBLE BAR C N HOLOMORPHIC MAPPINGS written by YIFEI PAN and published by . This book was released on 1990 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second part, we prove the following rigidity result for holomorphic mappings: Any holomorphic mapping that sends a non-Levi flat real hypersurface into a totally real submanifold is constant.
Download or read book Rigidity of Proper Holomorphic Mappings Between Bounded Symmetric Domains written by Zhenhan Tu and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Rigidity of Proper Holomorphic Mappings Between Bounded Symmetric Domains" by 涂振漢, Zhenhan, Tu, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. DOI: 10.5353/th_b4257564 Subjects: Symmetric spaces, Hermitian Holomorphic mappings Lie groups
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 On proper holomorphic mappings written by Zhiqiang Wu and published by . This book was released on 1991 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Proper Holomorphic Mappings Between Balls written by Dekang Xu and published by . This book was released on 2006 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Extending Proper Holomorphic Mappings of Positive Codimension written by Franc Forstnerič and published by . This book was released on 1987 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Manifolds and Holomorphic Mappings written by Shoshichi Kobayashi and published by World Scientific. This book was released on 2005 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections ?invariant metrics and pseudo-distances? and ?hyperbolic complex manifolds? within the section ?holomorphic mappings?. The invariant distance introduced in the first edition is now called the ?Kobayashi distance?, and the hyperbolicity in the sense of this book is called the ?Kobayashi hyperbolicity? to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Download or read book The Cauchy Transform Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 2015-11-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f
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 116 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.
