Analysis of degenerations and singularities of Kleinian groups and complex dynamics

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340028
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: SHIGA Hiroshige 東京工業大学, 理工学研究科, 教授 (10154189)
• Co-Investigator(Kenkyū-buntansha): AIKAWA Hiroaki 北海道大学, 大学院理学研究院, 教授 (20137889) ; SHISHIKURA Mitsuhiro 京都大学, 大学院理学研究科, 教授 (70192606) ; SUGAWA Toshiyuki 東北大学, 情報科学研究科, 教授 (32235858) ; ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203) ; OHSHIKA Ken'ichi 大阪大学, 大学院理学研究科, 教授 (70183325)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: Klein群 / リーマン面 / タイヒミュラー空間 / 複素力学系 / 複素解析 / 国際研究者交流 / 国際情報交換 / 多国籍

Outline of Final Research Achievements

By developing the research of the complex structure of the deformation space of a Kleinian group, we find many complex analytic properties of the deformation space. We also find a relationship between the infectivity radius of a point in the moduli space and the hyperbolic structure as the point tends to the boundary. In the complex dynamics, we find new phenomenon on the structure of invariant sets near indifferent fixed points. A progress on the boundary Harnack principle on singular domains is done and some estimates about hyperbolic metrics with cone singularities are obtained.

Free Research Field

数物系科学