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Author : W. Stoll
Publisher : Springer
ISBN 13 : 3540362878
Total Pages : 269 pages
Book Rating : 4.5/5 (43 download)
Download or read book Value Distribution of Holomorphic Maps into Compact Complex Manifolds written by W. Stoll and published by Springer. This book was released on 2006-11-15 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Wilhelm Stoll
Publisher :
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.F/5 ( download)
Download or read book Value Distribution of Holomorphic Maps Into Compact Complex Manifolds written by Wilhelm Stoll and published by . This book was released on 1970 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Phillip A. Griffiths
Publisher : Princeton University Press
ISBN 13 : 140088148X
Total Pages : 112 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 112 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 : I. Laine
Publisher : Springer
ISBN 13 : 354039480X
Total Pages : 256 pages
Book Rating : 4.5/5 (43 download)
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:
Author : G.M. Khenkin
Publisher : Springer Science & Business Media
ISBN 13 : 364261308X
Total Pages : 265 pages
Book Rating : 4.6/5 (426 download)
Download or read book Several Complex Variables III written by G.M. Khenkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
Author : Wilhelm Stoll
Publisher : Springer Science & Business Media
ISBN 13 : 3663052923
Total Pages : 358 pages
Book Rating : 4.6/5 (63 download)
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.
Author : Toshiki Mabuchi
Publisher : World Scientific
ISBN 13 : 9789810220679
Total Pages : 268 pages
Book Rating : 4.2/5 (26 download)
Download or read book Geometry and Analysis on Complex Manifolds written by Toshiki Mabuchi and published by World Scientific. This book was released on 1994 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.
Author : Grigor A. Barsegian
Publisher : Springer Science & Business Media
ISBN 13 : 1402079516
Total Pages : 331 pages
Book Rating : 4.4/5 (2 download)
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.
Author : Hans Grauert
Publisher : Springer
ISBN 13 : 3540398295
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)
Download or read book Complex Analysis and Algebraic Geometry written by Hans Grauert and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Toshiki Mabuchi
Publisher : World Scientific
ISBN 13 : 9814501220
Total Pages : 261 pages
Book Rating : 4.8/5 (145 download)
Download or read book Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday written by Toshiki Mabuchi and published by World Scientific. This book was released on 1994-12-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.
Author : Paul Alan Vojta
Publisher : Springer
ISBN 13 : 3540474528
Total Pages : 141 pages
Book Rating : 4.5/5 (44 download)
Download or read book Diophantine Approximations and Value Distribution Theory written by Paul Alan Vojta and published by Springer. This book was released on 2006-11-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3030690563
Total Pages : 430 pages
Book Rating : 4.0/5 (36 download)
Download or read book Minimal Surfaces from a Complex Analytic Viewpoint written by Antonio Alarcón and published by Springer Nature. This book was released on 2021-03-10 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Author : Shiu-yuen Cheng
Publisher : World Scientific
ISBN 13 : 9814499978
Total Pages : 732 pages
Book Rating : 4.8/5 (144 download)
Download or read book Mathematician And His Mathematical Work, A: Selected Papers Of S S Chern written by Shiu-yuen Cheng and published by World Scientific. This book was released on 1996-09-07 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.
Author : Phillip Griffiths
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820865
Total Pages : 694 pages
Book Rating : 4.8/5 (28 download)
Download or read book Selected Works of Phillip A. Griffiths with Commentary written by Phillip Griffiths and published by American Mathematical Soc.. This book was released on 2003 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized according to the subject matter, this title provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.
Author :
Publisher :
ISBN 13 :
Total Pages : 718 pages
Book Rating : 4.:/5 (327 download)
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:
Author : National Science Foundation (U.S.)
Publisher :
ISBN 13 :
Total Pages : 720 pages
Book Rating : 4.:/5 (3 download)
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:
