Integrated Study of Complex Analytic Structure

2001年10月30日至11月5日在京都/奈良举行的冈清百年诞辰纪念会议上，京都/奈良2001年11月6日至8日，2000年的第一届数学年会主要是在本基金的赞助下举行的，许多著名的多变量复分析数学家参加了这次会议，并取得了很大的成果，日本在这方面的研究水平最高。通过最新研究信息和想法的交流，再次确认了该计划的方法。结果是如此丰富，所获得的信息在整个项目中发挥了重要作用，并在该研究基金的支持下由日本数学学会出版了论文集。本研究计划的主要课题是“复解析结构”，特别是多变量Nevanlinna理论，伪凸域，复流形理论，.目前R ...更多信息 该计划由研究主题的调查人员与研究合作者共同执行。本项目取得了许多优秀的成果，以下只是部分成果：建立了全纯曲线为半交换簇的第二主要定理的最佳形式，以亚纯函数为目标的第二主要定理最好地完善了Nevanlinna猜想;构造了满足算术有限性的小林双曲射影超曲面，用自同构群构造了C^κ×（C^*）^l，C^κ×B^l的单值化定理，一维复动力学重整化中的压缩定理;强伪凸域上全纯函数的L^2-扩张定理的进一步改进，代数簇族的（下半）连续性，更高级的Kuranishi程序，保持器连续边界函数Dirichlet解的保持器连续性，以及不存在保持Lipschitz连续的域.少

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