2004 Fiscal Year Final Research Report Summary
Integrated Study of Complex Analytic Structure
| Project/Area Number |
13304009
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | The University of Tokyo |
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Principal Investigator |
NOGUCHI Junjiro University of Tokyo, Professor, 大学院・数理科学研究科, 教授 (20033920)
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| Co-Investigator(Kenkyū-buntansha) |
OHSAWA Takeo Nagoya University, Professor, 大学院・多元数理科学研究科, 教授 (30115802)
KAZAMA Hideaki Kyushu University, Professor, 大学院・数理学研究院, 教授 (10037252)
AIKAWA Hiroai Shimane University, Professor, 総合理工学部, 教授 (20137889)
HIRACHI Kengo University of Tokyo, Associate Professor, 大学院・数理科学研究科, 助教授 (60218790)
YOSHIKAWA Kenich University of Tokyo, Associate Professor, 大学院・数理科学研究科, 助教授 (20242810)
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| Project Period (FY) |
2001 – 2004
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| Keywords | several complex variables / geometric complex analysis / Kobayashi hyperbolic manifold / value distribution / pseudoconvex domain / moduli space / complex dynamics / Teichmuller space |
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| Research Abstract |
In the first year 2001 of this research program Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001, October 30-November 5,Kyoto/November 6-8,Nara, was held mainly under the sponsorship of the present fund. A number of celebrated mathematicians in complex analysis in several variables participated in it and it was a great outcome that the works on this subject in Japan showed the highest level of research. Through the exchanges of latest research information and ideas the approach of this program was reconfirmed. The results were so ample that the obtained information have played important roles all through this project, and the proceedings was published from Mathematical Society of Japan by the support of this research fund.
The main subject of the present research program is "Complex Analytic Structure", especially Nevanlinna theory in several variables, pseudoconvex domains, complex manifold theory,..., etc. The present r
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esearch has been executed by investigators attached to the research themes joint with research cooperators. All the research results were summarized by the representative investigator.
There are many excellent results obtained through the present project and the following are only partial ones : Establishing the second main theorem for holomorphic curves into semi-abelian varieties in the best form ; the second main theorem for meromorphic functions as targets best refined the Nevanlinna conjecture ; a construction of Kobayashi hyperbolic projective hypersurfaces satisfying the arithmetic finiteness property; uniformization theorems for C^κ×(C^*)^l, C^κ×B^l by automorphism groups ; the contraction theorem in the renormalization of one-dimensional complex dynamics ; further refinement of L^2-extension theorem of holomorphic functions in strongly pseudoconvex domains that have important applications ; (lowersemi-) continuity of plurigenera for family of algebraic varieties ; More advanced Kuranishi program ; Holder continuity of Dirichlet solutions for Holder continuous boundary functions and the non-existence of domains preserving Lipschitz continuity. Less
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