Research on the Teichmuller spaces of fractal structures

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04925
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara Women's University
• Principal Investigator: Taniguchi Masahiko 奈良女子大学, 名誉教授 (50108974)
• Co-Investigator(Renkei-kenkyūsha): Fujimura MASAYO 防衛大学校, 総合教育学群, 准教授 (00531758) ; Matsuzaki KATSUHIKO 早稲田大学, 教育・総合科学学術院, 教授 (80222298) ; Fujikawa EGE 千葉大学, 大学院理学研究科, 准教授 (80433788)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: タイヒミュラー空間 / フラクタル集合 / 擬等角写像

Outline of Final Research Achievements

We formulate the concept of the Teichmuller space of a fractal structure and establish the fundamental theory on it. This is one of the main purposes of this research project. More precisely, we introduce the Teichmuller space of a countable set of points associated with the fractal structure on a general Riemann surface. Furthermore, we show that such a space admits a natural complex analytic structure if the fractal structure possesses standard bounded geometry.
The second purpose of this research project is to introduce geometric global coordinates for such a Teichmuller space. On this point, for several important cases such as the iterated function systems by Mobius transformations, Kleinian group actions, and infinitely generated Koebe group actions, we introduce natural geometric global coordinates on the Teichmuller space of the corresponding fractal structure, and obtain a global representation of it.

Free Research Field

複素解析