Integrated Study of Complex Analytic Structure

点击翻译按钮获取中文摘要

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 … More 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