Value distribution theory of meromorphic functions based on diffusion processes

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540192
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Keio University
• Principal Investigator: ATSUJI Atsushi 慶應義塾大学, 経済学部, 教授 (00221044)
• Co-Investigator(Renkei-kenkyūsha): TAMURA Yozo 慶應義塾大学, 理工学部, 教授 (50171905) ; AIHARA Yoshohiro 福島大学, 人間発達文化学類, 教授 (60175718)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 複素解析 / 拡散過程 / 正則写像 / 値分布論 / ネヴァンリンナ理論 / 複素葉層構造

Outline of Final Research Achievements

We continuously investigate the theory of value distribution of holomorphic maps using probabilistic technique. We found Nevanlinna theory based on diffusion processes in our previous works and we have developed it. In this project we try to apply our theory to new and wider objects than our previous research. Our main object is the value distribution of holomorphic maps on complex foliated spaces. We obtained some results on value distribution of these maps, for instance, we showed a Picard type theorem of meromorphic functions associated with complex foliation structure.

Free Research Field

数学