Distribution Of Values Of Holomorphic Mappings

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Distribution of Values of Holomorphic Mappings

Author : Boris Vladimirovich Shabat
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898116
Total Pages : 236 pages
Book Rating : 4.8/5 (981 download)

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Book Synopsis Distribution of Values of Holomorphic Mappings by : Boris Vladimirovich Shabat

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.

Value Distribution Theory

Author : I. Laine
Publisher : Springer
ISBN 13 : 354039480X
Total Pages : 256 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Value Distribution Theory by : I. Laine

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:

Value Distribution Theory for Meromorphic Maps

Author : Wilhelm Stoll
Publisher : Springer Science & Business Media
ISBN 13 : 3663052923
Total Pages : 358 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis Value Distribution Theory for Meromorphic Maps by : Wilhelm Stoll

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.

Value Distribution Theory and Its Applications

Author : Chung-Chun Yang
Publisher : American Mathematical Soc.
ISBN 13 : 0821850253
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Value Distribution Theory and Its Applications by : Chung-Chun Yang

Download or read book Value Distribution Theory and Its Applications written by Chung-Chun Yang and published by American Mathematical Soc.. This book was released on 1983 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Geometric Analysis in Pohang

Author : Kang-Tae Kim
Publisher : American Mathematical Soc.
ISBN 13 : 0821809571
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Complex Geometric Analysis in Pohang by : Kang-Tae Kim

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.

Entire Functions of Several Complex Variables

Author : Pierre Lelong
Publisher : Springer Science & Business Media
ISBN 13 : 3642703445
Total Pages : 283 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Entire Functions of Several Complex Variables by : Pierre Lelong

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.

European Congress of Mathematics

Author : Ari Laptev
Publisher : European Mathematical Society
ISBN 13 : 9783037190098
Total Pages : 906 pages
Book Rating : 4.1/5 (9 download)

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Book Synopsis European Congress of Mathematics by : Ari Laptev

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.

Entire Holomorphic Mappings in One and Several Complex Variables

Author : Phillip Griffiths
Publisher : Princeton University Press
ISBN 13 : 9780691081724
Total Pages : 116 pages
Book Rating : 4.0/5 (817 download)

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Book Synopsis Entire Holomorphic Mappings in One and Several Complex Variables by : Phillip Griffiths

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.

Contributions to Several Complex Variables

Author : Alan Howard
Publisher : Springer Science & Business Media
ISBN 13 : 3663068161
Total Pages : 357 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis Contributions to Several Complex Variables by : Alan Howard

Download or read book Contributions to Several Complex Variables written by Alan Howard and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1960 Wilhelm Stoll joined the University of Notre Dame faculty as Professor of Mathematics, and in October, 1984 the university acknowledged his many years of distinguished service by holding a conference in complex analysis in his honour. This volume is the proceedings of that conference. It was our priviledge to serve, along with Nancy K. Stanton, as conference organizers. We are grateful to the College of Science of the University of Notre Dame and to the National Science Foundation for their support. In the course of a career that has included the publication of over sixty research articles and the supervision of eighteen doctoral students, Wilhelm Stoll has won the affection and respect of his colleagues for his diligence, integrity and humaneness. The influence of his ideas and insights and the subsequent investigations they have inspired is attested to by several of the articles in the volume. On behalf of the conference partipants and contributors to this volume, we wish Wilhelm Stoll many more years of happy and devoted service to mathematics. Alan Howard Pit-Mann Wong VII III ~ c: ... ~ c: o U CI> .r. ~ .... o e ::J ~ o a:: a. ::J o ... (.!:J VIII '" Q) g> a. '" Q) E z '" ..... o Q) E Q) ..c eX IX Participants on the Group Picture Qi-keng LU, Professor, Chinese Academy of Science, Peking, China.

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

Author : Junjiro Noguchi
Publisher : Springer Science & Business Media
ISBN 13 : 4431545719
Total Pages : 425 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by : Junjiro Noguchi

Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.

Hyperbolic Complex Spaces

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3662035820
Total Pages : 480 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Hyperbolic Complex Spaces by : Shoshichi Kobayashi

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.

Unicity of Meromorphic Mappings

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 1475737750
Total Pages : 472 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Unicity of Meromorphic Mappings by : Pei-Chu Hu

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.

Summaries of Projects Completed in Fiscal Year ...

Author : National Science Foundation (U.S.)
Publisher :
ISBN 13 :
Total Pages : 720 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Summaries of Projects Completed in Fiscal Year ... by : National Science Foundation (U.S.)

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:

Summaries of Projects Completed in Fiscal Year ...

Author :
Publisher :
ISBN 13 :
Total Pages : 718 pages
Book Rating : 4.:/5 (327 download)

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Book Synopsis Summaries of Projects Completed in Fiscal Year ... by :

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:

Summaries of Projects Completed

Author : National Science Foundation (U.S.)
Publisher :
ISBN 13 :
Total Pages : 728 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Summaries of Projects Completed by : National Science Foundation (U.S.)

Download or read book Summaries of Projects Completed written by National Science Foundation (U.S.) and published by . This book was released on with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis

Author : J. Eells
Publisher : Springer
ISBN 13 : 3540393668
Total Pages : 435 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Complex Analysis by : J. Eells

Download or read book Complex Analysis written by J. Eells and published by Springer. This book was released on 2006-11-15 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Value Distribution Theory Related to Number Theory

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3764375698
Total Pages : 546 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Value Distribution Theory Related to Number Theory by : Pei-Chu Hu

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.