Value distribution theory of analytic maps, Diophantine approximation and intersections of analytic cycles

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340029
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: NOGUCHI Junjiro 東京大学, 数理(科)学研究科(研究院), 名誉教授 (20033920)
• Co-Investigator(Renkei-kenkyūsha): YAMANOI Katsutoshi 東京工業大学, 大学院理工学研究科, 准教授 (40335295) ; OHSAWA Takeo 名古屋大学, 大学院多元数理科学研究科, 教授 (30115802) ; TSUJI Hajime 上智大学, 理工学部, 教授 (30172000) ; HIRATA Noriko (KOHNO Noriko) 日本大学, 理工学部, 教授 (90215195) ; ASUKE Taro 東京大学, 大学院数理科学研究科, 准教授 (30294515) ; HAMANO Sachiko 福島大学, 人間発達文化学類, 准教授 (10469588)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 解析学 / 関数論 / 複素解析学 / 値分布論 / Vojta予想

Outline of Final Research Achievements

In Nevanlinna theory of several complex variables of the second main theorem type has been of central importance. We, jointly with Winkelmann (Bochum Univ.) and Yamanoi (T.I.T.) obtained results, most advanced so far now. Jointly with Corvaja (Udine Univ.) we obtained an application and an arithmetic analogy of this result, which is of very new type and of interest; in the course we extended, certain classical result of Lang-Ax for entire holomorphic curves (originally only for 1-parameter subgroups). We, jointly with Abe (Hiroshima Univ.) and Hamano (Fukushima Univ.), solved Oka's extra zero problem which was posed by K. Oka in his posthumous paper (1945) for a generalization of Oka's principle.
In Oka-Cartan theory, which is the fundamental part of the present research, a number of improvements and simplifications were obtained. Two monographs including those results were published, and some new themes have come out.

Free Research Field

多変数複素解析学