2005 Fiscal Year Final Research Report Summary
QUANTITATIVE RESEARCH OF DEFICIENCIES OF MEROMORPFIC MAPPINGS AND EXCEPTIONAL MAPPINGS
| Project/Area Number |
15540151
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Yamagata University |
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Principal Investigator |
MORI Seiki YAMAGATA UNIVERSITY, FAC.SCI., PROFESSOR, 理学部, 教授 (80004456)
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| Co-Investigator(Kenkyū-buntansha) |
AIHARA Yoshihiro NUMAZU COLL., TECH., PROFESSOR, 教授 (60175718)
NAKADA Masami YAMAGATA UNIVERSITY, FAC.SCI., PROFESSOR, 理学部, 教授 (20007173)
KAWAMURA Shinzo YAMAGATA UNIVERSITY, FAC.SCI., PROFESSOR, 理学部, 教授 (50007176)
SATO Enji YAMAGATA UNIVERSITY, FAC.SCI., PROFESSOR, 理学部, 教授 (80107177)
MIZUHARA Takahiro YAMAGATA UNIVERSITY, FAC.SCI., PROFESSOR, 理学部, 教授 (80006577)
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| Project Period (FY) |
2003 – 2005
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| Keywords | value distribution theory / meromorphic mapping / defect / unicity theorem / hypersurface / complex dynamical system / complex projective space / function space |
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| Research Abstract |
The head investigator Mori researched a sparsity of meromorphic mappings with defects. He obtained elimination theorems of defects of hypersurfaces or rational moving targets of a meromorphic mapping into P^n(C) by a small deformation, and he also proved that mappings without defects are dense in a space of transcendental meromorphic mappings. He and an investigator Aihara also obtained results that for any hypersurface of degree d on P^n(C), we can construct an algebraically nondegenerate meromorphic mapping with a preassaigned deficiency in an interval (0,α), where α>0 depends only on d. Mori also studied on uniqueness theorems of meromorphic functions. There are many results on uniqueness sets, but it seems that there are few results on uniqueness domains. We are going to find an unbounded domain in C such that a uniqueness theorem holds under the condition restricted on the domain. Mori, Lin and Tohge gave a uniqueness theorem under the condition restricted on an angular domain, an
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d the paper was submitted. An investigator Aihara obtained several conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained a condition under which two analytic ramified covering spaces are identical. This is a geometric extension of a uniqueness theorem of algebroid functions. Nakada investigated a complex dynamics of Blachke products like rational functions, especially, an estimate of a Hausdorff dimension and the invariance of Julia set under Euclidean congruent transformation. Sekigawa investigated a limit set of a sequence of Moebius transformations acting on C, and also he treated Moebius transformations acting on a general dimension space. He also studied an expression of Moebius transformations using Cliford matrix, and its applications. Kawamura studied an orbit of probabilistic density function, and also he gave a proof of a properties of topological conjugate maps on a group of Tent maps, after computer simulation. Sato gave a generalization of relation between Jacobian orthogonal system and an operators on a function space and an operators on Hankel transformations. Mizuhara proved a weak decomposition theorem related to a function on a generalized Morrey space and Block and Calderon-Zygmund operators. Less
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