Distribution Of Values Of Holomorphic Mappings
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Distribution Of Values Of Holomorphic Mappings
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Author : Boris Vladimirovich Shabat
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-31
Distribution Of Values Of Holomorphic Mappings written by Boris Vladimirovich Shabat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-31 with Mathematics categories.
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.
Value Distribution Of Holomorphic Maps Into Compact Complex Manifolds
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Author : W. Stoll
language : en
Publisher:
Release Date : 2014-09-01
Value Distribution Of Holomorphic Maps Into Compact Complex Manifolds written by W. Stoll and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Entire Holomorphic Mappings In One And Several Complex Variables
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Author : Phillip Griffiths
language : en
Publisher: Princeton University Press
Release Date : 1976-02-21
Entire Holomorphic Mappings In One And Several Complex Variables written by Phillip Griffiths and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-02-21 with Mathematics categories.
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.
Value Distribution Of Holomorphic Maps Into Compact Complex Manifolds
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Author : W. Stoll
language : en
Publisher: Springer
Release Date : 2006-11-15
Value Distribution Of Holomorphic Maps Into Compact Complex Manifolds written by W. Stoll and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Value Distribution Theory Of The Gauss Map Of Minimal Surfaces In Rm
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Author : Hirotaka Fujimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Value Distribution Theory Of The Gauss Map Of Minimal Surfaces In Rm written by Hirotaka Fujimoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.
Unicity Of Meromorphic Mappings
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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Unicity Of Meromorphic Mappings written by Pei-Chu Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.
Value Distribution On Parabolic Spaces
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Author : W. Stoll
language : en
Publisher: Springer
Release Date : 2006-11-15
Value Distribution On Parabolic Spaces written by W. Stoll and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Value Distribution Theory And Related Topics
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Author : Grigor A. Barsegian
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
Value Distribution Theory And Related Topics written by Grigor A. Barsegian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Mathematics categories.
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.
Conformal Mappings And Boundary Value Problems
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Author : Guo-Chun Wen
language : en
Publisher: American Mathematical Soc.
Release Date :
Conformal Mappings And Boundary Value Problems written by Guo-Chun Wen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Translated from the Chinese. Conformal mapping and boundary value problems are two major branches of complex function theory. The former is the geometric theory of analytic functions, and the latter is the analysis theory governing the close relationship between abstract theory and many concrete problems. Topics include applications of Cauchy type integrals, the Hilbert boundary value problem, quasiconformal mappings, and basic boundary value problems for harmonic functions. Annotation copyright by Book News, Inc., Portland, OR
Value Distribution Theory For Meromorphic Maps
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Author : Wilhelm Stoll
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Value Distribution Theory For Meromorphic Maps written by Wilhelm Stoll and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.