The Equidistribution Theory Of Holomorphic Curves

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The Equidistribution Theory Of Holomorphic Curves

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Author : Hongxi Wu
language : en
Publisher: Princeton University Press
Release Date : 1970-02-21

The Equidistribution Theory Of Holomorphic Curves written by Hongxi Wu 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 1970-02-21 with Mathematics categories.

This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.

The Equidistribution Theory Of Holomorphic Curves

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Author : Hung-his Wu
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

The Equidistribution Theory Of Holomorphic Curves written by Hung-his Wu 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 2016-03-02 with Mathematics categories.

This work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.

The Equidistribution Theory Of Holomorphic Curves

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Author : Hung-hsi Wu
language : en
Publisher:
Release Date :

The Equidistribution Theory Of Holomorphic Curves written by Hung-hsi Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Analytic functions categories.

Nevanlinna Theory In Several Complex Variables And Diophantine Approximation

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Author : Junjiro Noguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-09

Nevanlinna Theory In Several Complex Variables And Diophantine Approximation written by Junjiro Noguchi 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 2013-12-09 with Mathematics categories.

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.

Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition

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Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2021-03-10

Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.

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.

Nevanlinna Theory

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Author : Kunihiko Kodaira
language : en
Publisher: Springer
Release Date : 2017-12-15

Nevanlinna Theory written by Kunihiko Kodaira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Mathematics categories.

This book deals with the classical theory of Nevanlinna on the value distribution of meromorphic functions of one complex variable, based on minimum prerequisites for complex manifolds. The theory was extended to several variables by S. Kobayashi, T. Ochiai, J. Carleson, and P. Griffiths in the early 1970s. K. Kodaira took up this subject in his course at The University of Tokyo in 1973 and gave an introductory account of this development in the context of his final paper, contained in this book. The first three chapters are devoted to holomorphic mappings from C to complex manifolds. In the fourth chapter, holomorphic mappings between higher dimensional manifolds are covered. The book is a valuable treatise on the Nevanlinna theory, of special interests to those who want to understand Kodaira's unique approach to basic questions on complex manifolds.

Entire Holomorphic Mappings In One And Several Complex Variables Am 85 Volume 85

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Author : Phillip A. Griffiths
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Entire Holomorphic Mappings In One And Several Complex Variables Am 85 Volume 85 written by Phillip A. 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 2016-03-02 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 Theory Related To Number Theory

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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-06

Value Distribution Theory Related To Number Theory 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 2006-10-06 with Mathematics categories.

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.

Hyperbolic Manifolds And Holomorphic Mappings An Introduction Second Edition

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Author : Shoshichi Kobayashi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-11-02

Hyperbolic Manifolds And Holomorphic Mappings An Introduction Second Edition written by Shoshichi Kobayashi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-02 with Mathematics categories.

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.

Value Distribution Theory And Its Applications

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Author : Chung-Chun Yang
language : en
Publisher: American Mathematical Soc.
Release Date : 1983

Value Distribution Theory And Its Applications written by Chung-Chun Yang 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 1983 with Mathematics categories.