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Author : Leopoldo Nachbin
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.3/5 (91 download)
Download or read book Some Aspects of Holomorphic Mappings written by Leopoldo Nachbin and published by . This book was released on 1968 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Phillip A. Griffiths
Publisher : Princeton University Press
ISBN 13 : 140088148X
Total Pages : 110 pages
Book Rating : 4.4/5 (8 download)
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.
Author : Mark Elin
Publisher : Springer
ISBN 13 : 3030050203
Total Pages : 229 pages
Book Rating : 4.0/5 (3 download)
Download or read book Numerical Range of Holomorphic Mappings and Applications written by Mark Elin and published by Springer. This book was released on 2019-03-11 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.
Author : Sergey Pinchuk
Publisher : Springer Nature
ISBN 13 : 3031371496
Total Pages : 217 pages
Book Rating : 4.0/5 (313 download)
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.
Author : Phillip Griffiths
Publisher : Princeton University Press
ISBN 13 : 0691081727
Total Pages : 111 pages
Book Rating : 4.6/5 (91 download)
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.
Author : Boris Vladimirovich Shabat
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898116
Total Pages : 236 pages
Book Rating : 4.8/5 (981 download)
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.
Author : Franc Forstnerič
Publisher : Springer Science & Business Media
ISBN 13 : 3642222501
Total Pages : 501 pages
Book Rating : 4.6/5 (422 download)
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.
Author : W.-Y. Hsiang
Publisher : Springer Science & Business Media
ISBN 13 : 1461381096
Total Pages : 258 pages
Book Rating : 4.4/5 (613 download)
Download or read book The Chern Symposium 1979 written by W.-Y. Hsiang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. • . . . • . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . • . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER .
Author : Franc Forstnerič
Publisher : Springer
ISBN 13 : 3319610589
Total Pages : 569 pages
Book Rating : 4.3/5 (196 download)
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.
Author : 陳耿彥
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (57 download)
Download or read book Some Results on Holomorphic Mappings on Cn written by 陳耿彥 and published by . This book was released on 2003 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bayram Sahin
Publisher : Academic Press
ISBN 13 : 0128044101
Total Pages : 362 pages
Book Rating : 4.1/5 (28 download)
Download or read book Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications written by Bayram Sahin and published by Academic Press. This book was released on 2017-01-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore's classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps. - Systematically reviews and references modern literature in Riemannian maps - Provides rigorous mathematical theory with applications - Presented in an accessible reading style with motivating examples that help the reader rapidly progress
Author : Alan Trinler Huckleberry
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.F/5 ( download)
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:
Author : Marcus Wono Setya-Budhi
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (318 download)
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}
Author : Shoshichi Kobayashi
Publisher : World Scientific
ISBN 13 : 9812564969
Total Pages : 161 pages
Book Rating : 4.8/5 (125 download)
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.
Author : R. Michael Range
Publisher : Springer Science & Business Media
ISBN 13 : 1475719183
Total Pages : 405 pages
Book Rating : 4.4/5 (757 download)
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Author : Leopoldo Nachbin
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.F/5 ( download)
Download or read book Topology on Spaces of Holomorphic Mappings written by Leopoldo Nachbin and published by . This book was released on 1969 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R.C. Gunning
Publisher : Routledge
ISBN 13 : 1351436902
Total Pages : 250 pages
Book Rating : 4.3/5 (514 download)
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 250 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.
