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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 : Wilhelm Stoll
Publisher :
ISBN 13 :
Total Pages : 267 pages
Book Rating : 4.:/5 (741 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 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : 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 : W. Stoll
Publisher : Springer
ISBN 13 : 3540373063
Total Pages : 223 pages
Book Rating : 4.5/5 (43 download)
Download or read book Value Distribution on Parabolic Spaces written by W. Stoll and published by Springer. This book was released on 2006-11-15 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : J. Eells
Publisher : Springer
ISBN 13 : 3540393668
Total Pages : 435 pages
Book Rating : 4.5/5 (43 download)
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:
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 : Chung-Chun Yang
Publisher : American Mathematical Soc.
ISBN 13 : 0821850253
Total Pages : 253 pages
Book Rating : 4.8/5 (218 download)
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 253 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 : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475719450
Total Pages : 278 pages
Book Rating : 4.4/5 (757 download)
Download or read book Introduction to Complex Hyperbolic Spaces written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.
Author : Shiing-shen Chern
Publisher : Springer Science & Business Media
ISBN 13 : 1468493442
Total Pages : 158 pages
Book Rating : 4.4/5 (684 download)
Download or read book Complex Manifolds without Potential Theory written by Shiing-shen Chern and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#
Author : Wilhelm Stoll
Publisher : Princeton University Press
ISBN 13 : 1400881889
Total Pages : 128 pages
Book Rating : 4.4/5 (8 download)
Download or read book Invariant Forms on Grassmann Manifolds. (AM-89), Volume 89 written by Wilhelm Stoll and published by Princeton University Press. This book was released on 2016-03-02 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers a contribution in the geometric form of the theory of several complex variables. Since complex Grassmann manifolds serve as classifying spaces of complex vector bundles, the cohomology structure of a complex Grassmann manifold is of importance for the construction of Chern classes of complex vector bundles. The cohomology ring of a Grassmannian is therefore of interest in topology, differential geometry, algebraic geometry, and complex analysis. Wilhelm Stoll treats certain aspects of the complex analysis point of view. This work originated with questions in value distribution theory. Here analytic sets and differential forms rather than the corresponding homology and cohomology classes are considered. On the Grassmann manifold, the cohomology ring is isomorphic to the ring of differential forms invariant under the unitary group, and each cohomology class is determined by a family of analytic sets.
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 : Junjiro Noguchi
Publisher : Springer Science & Business Media
ISBN 13 : 4431545719
Total Pages : 425 pages
Book Rating : 4.4/5 (315 download)
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.
Author : Min Ru
Publisher : World Scientific
ISBN 13 : 9811233527
Total Pages : 443 pages
Book Rating : 4.8/5 (112 download)
Download or read book Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) written by Min Ru and published by World Scientific. This book was released on 2021-03-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory.
