Overview
- Authors:
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Pei-Chu Hu
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Shandong University, Shandong, P.R. China
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Chung-Chun Yang
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University of Science and Technology, Clearwater Bay, Hong Kong, China
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Table of contents (7 chapters)
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Front Matter
Pages i-viii
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- Pei-Chu Hu, Chung-Chun Yang
Pages 1-31
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- Pei-Chu Hu, Chung-Chun Yang
Pages 33-75
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- Pei-Chu Hu, Chung-Chun Yang
Pages 77-113
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- Pei-Chu Hu, Chung-Chun Yang
Pages 115-138
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- Pei-Chu Hu, Chung-Chun Yang
Pages 139-175
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- Pei-Chu Hu, Chung-Chun Yang
Pages 177-223
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- Pei-Chu Hu, Chung-Chun Yang
Pages 225-241
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Back Matter
Pages 243-295
About this book
Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open).
Authors and Affiliations
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Shandong University, Shandong, P.R. China
Pei-Chu Hu
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University of Science and Technology, Clearwater Bay, Hong Kong, China
Chung-Chun Yang
