Analysis of extremal Riemann surfaces and Klein surfaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400147
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Aichi Institute of Technology
• Principal Investigator: NAKAMURA Gou 愛知工業大学, 工学部, 教授 (50319208)
• Co-Investigator(Renkei-kenkyūsha): NAKANISHI Toshihiro 島根大学, 総合理工学研究科, 教授 (00172354)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 複素解析 / リーマン面 / クライン面 / 極値的円板 / 自己同型群 / モジュライ空間 / 解析学

Outline of Final Research Achievements

In the moduli space of closed Riemann surfaces of genus g, where g is greater than 1, we studied examples of those admitting a disk of the largest radius determined by genus (extremal disk). By considering characterization of their Fuchsian group representations and the structure of symmetricity, we obtained some results such as the groups of automorphisms and the locus of those surfaces in the Teichmuller space. We also made a similar analysis of non-orientable extremal Klein surfaces by considering their NEC group representations, and obtained some results.

Free Research Field

数物系科学