Integrated Study of Complex Analytic Structure

在本研究计划的第一年2001年，主要在本基金的赞助下，于京都/奈良（2001年10月30日至11月5日，京都/奈良，11月6日至8日）举行了冈清百周年复变分析纪念会议。许多在多变量复杂分析领域的著名数学家参与其中，这是一个伟大的成果，日本在这一课题上的工作显示了最高的研究水平。通过最新的研究信息和思想的交流，这个项目的方法得到了再次确认。结果非常充分，所获得的信息在整个项目中发挥了重要作用，论文在该研究基金的支持下由日本数学学会发表。本课题的主要研究方向是“复解析结构”，特别是多变量内万林纳理论、伪凸域、复流形理论等。等。更多的研究是由附属于研究主题的研究人员与研究合作者共同进行的。所有的研究结果由代表研究者进行总结。本课题得到了许多优秀的结果，以下只是部分的结果：建立全纯曲线成半阿贝尔变的最佳形式的第二主要定理；亚纯函数作为目标的第二个主要定理最好地完善了Nevanlinna猜想；满足算术有限性的Kobayashi双曲射影超曲面的构造C^κ x (C^*)^l， C^κ×B^l的自同构群的一致化定理一维复杂动力学重整化中的收缩定理在强伪凸域上对全纯函数的L^2扩展定理的进一步改进代数变种科多属的（下半）连续性更先进的Kuranishi程序；霍尔德连续边界函数Dirichlet解的霍尔德连续性及保持Lipschitz连续性的不存在性。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