Value Distribution on Parabolic Spaces

Value Distribution on Parabolic Spaces

Further they require that t has only finitely many critical values. These requirements are unnecessary and excessively restrictive. A modification of a parabolic space may fail to be parabolic under these requirements.

Author: W. Stoll

Publisher: Springer

ISBN: 9783540373063

Category: Mathematics

Page: 216

View: 354

Categories: Mathematics

Value Distribution Theory

Value Distribution Theory

Stoll, W. : Aspects of value distribution theory in several complex variables. Bull. Amer. Math. Soc. 83 (l.8 77), 166 - 183. Stoll, W. : Value distribution theory on parabolic spaces. Lecture Notes in Mathematics 600, Springer-Verlag, ...

Author: I. Laine

Publisher: Springer

ISBN: 9783540394808

Category: Mathematics

Page: 250

View: 287

Categories: Mathematics

Value Distribution Theory and Its Applications

Value Distribution Theory and Its Applications

Chung-Chun Yang, Special Session on Value Distribution Theory and Its Applications. Proposition 3. l. ... Springer-Verlag, BerlinHeidelberg-New York, 1970. , Value distribution on parabolic spaces, Lecture Notes in Mathematics 600.

Author: Chung-Chun Yang

Publisher: American Mathematical Soc.

ISBN: 9780821850251

Category: Mathematics

Page: 253

View: 368

Categories: Mathematics

Introduction to Complex Hyperbolic Spaces

Introduction to Complex Hyperbolic Spaces

... Value Distribution Theory, Part B, Marcel Dekker, New York, 1974, [Stoll 5] W. STOLL, Value distribution theory for meromorphic maps, Vieweg, Aspects of Mathematics, 1985. [Stoll 6] W. STOLL, Value distribution on parabolic spaces, ...

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 9781475719451

Category: Mathematics

Page: 272

View: 471

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.
Categories: Mathematics

Distribution of Values of Holomorphic Mappings

Distribution of Values of Holomorphic Mappings

[ 5 ] About the value distribution of holomorphic maps into the projective space , Acta Math . 123 ( 1969 ) , 83-114 . [ 6 ] A Bézout estimate for ... [ 8 ] Value distribution on parabolic spaces , Lecture Notes in Math . , vol .

Author: Boris Vladimirovich Shabat

Publisher: American Mathematical Soc.

ISBN: 0821898116

Category: Mathematics

Page: 236

View: 639

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.
Categories: Mathematics

Several Complex Variables

Several Complex Variables

(3) L.) Let V = T(N, L) be the vector space of global holomorphic section of L. Let l be a hermitian metric on V. Take ai, ..., a, ... S. S. Chern, Holomorphic curves and minimal surfaces, VALUE DISTRIBUTION ON PARABOLIC SPACES 263.

Author: Raymond O'Neil Wells

Publisher: American Mathematical Soc.

ISBN: 9780821802502

Category: Mathematics

Page: 328

View: 144

Contains sections on Noncompact complex manifolds, Differential geometry and complex analysis, Problems in approximation, Value distribution theory, Group representation and harmonic analysis, Survey papers.
Categories: Mathematics

Contributions to Several Complex Variables

Contributions to Several Complex Variables

Math. Z. 57, 116-154 (1952). Stoll, W. , About the value distribution of holomorphic maps into projective space, Acta Math. 123, 83–114,01969). Stoll, W., Value distribution on parabolic spaces, Springer Lecture Notes Vol. 600 (1977).

Author: Alan Howard

Publisher: Springer Science & Business Media

ISBN: 9783663068167

Category: Mathematics

Page: 353

View: 518

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.
Categories: Mathematics

Hyperbolic Complex Spaces

Hyperbolic Complex Spaces

Z. 84 (1964), 154–218 [3] Aspects of value distribution theory in several complex variables. Bull. Amer. Math. Soc. 83 (1977), 166–183 [4] Value Distribution on Parabolic Spaces. Lecture Notes in Math.

Author: Shoshichi Kobayashi

Publisher: Springer Science & Business Media

ISBN: 9783662035825

Category: Mathematics

Page: 474

View: 848

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.
Categories: Mathematics

Value Distribution Theory and Related Topics

Value Distribution Theory and Related Topics

Stoll, W., Value distribution on parabolic spaces, Lecture Notes in Math., 600, Springer-Verlag, Berlin-New York, 1977. Ueno, K., Classification of algebraic varieties I, Compositio Math. 27 (1973), 277– 342.

Author: Grigor A. Barsegian

Publisher: Springer Science & Business Media

ISBN: 9781402079511

Category: Mathematics

Page: 333

View: 429

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.
Categories: Mathematics