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 Value Distribution Theory of Holomorphic Mappings written by J. Noguchi and published by . This book was released on 1997 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Value Distribution Theory written by I. Laine and published by Springer. This book was released on 2006-11-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Value Distribution Theory for Meromorphic Maps written by Wilhelm Stoll and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conformal Mappings and Boundary Value Problems written by Guo-Chun Wen and published by American Mathematical Soc.. This book was released on with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Value Distribution Theory and Related Topics written by Grigor A. Barsegian and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Arithmetic of Probability Distributions and Characterization Problems on Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and published by American Mathematical Soc.. This book was released on 1993 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Download or read book Arithmetic of Probability Distributions and Characterization Problems on Abelian Groups written by Gennadij M. Fel'dman and published by American Mathematical Soc.. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Download or read book Complex Geometric Analysis in Pohang written by Kang-Tae Kim and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the proceedings of a conference on the geometric analysis of several complex variables held at POSTECH in June 1997. The conference was attended by scienctists and students from around the globe. Each of the five plenary speakers at the conference gave a short course on a topic of current interest in the field. The lecture write-ups contain cogent and accessible information intended for a broad audience. The volume also includes a tutorial in several complex variables given by Kim and Krantz at the conference. This tutorial is geared toward helping the novice to understand the rest of the material in the book. The bibliographies of the papers give students and young mathematicians a valuable resource for future learning on the topic. This book provides a substantial overview on areas of current activity. Required background for understanding the text is a solid undergraduate education in mathematics and familiarity with first year graduate studies in real and complex analysis. Some exposure to geometry would be helpful. The book is also suitable for use as a supplemental course text.
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 Unicity of Meromorphic Mappings written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 European Congress of Mathematics written by Ari Laptev and published by European Mathematical Society. This book was released on 2005 with total page 906 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris, 1992, Budapest, 1996, and Barcelona, 2000, the Fourth European Congress of Mathematics took place in Stockholm, Sweden, June 27 to July 2, 2004, with 913 participants from 65 countries. Apart from seven plenary and thirty three invited lectures, there were six Science Lectures covering the most relevant aspects of mathematics in science and technology. Moreover, twelve projects of the EU Research Training Networks in Mathematics and Information Sciences, as well as Programmes from the European Science Foundation in Physical and Engineering Sciences, were presented. Ten EMS Prizes were awarded to young European mathematicians who have made a particular contribution to the progress of mathematics. Five of the prizewinners were independently chosen by the 4ECM Scientific Committee as plenary or invited speakers. The other five prizewinners gave their lectures in parallel sessions. Most of these contributions are now collected in this volume, providing a permanent record of so much that is best in mathematics today.
Download or read book Summaries of Projects Completed in Fiscal Year written by National Science Foundation (U.S.) and published by . This book was released on 1979 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summaries of Projects Completed in Fiscal Year written by and published by . This book was released on 1979 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt:
