2012 Fiscal Year Final Research Report
Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups
| Project/Area Number |
20340030
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Waseda University (2010-2012)
Okayama University (2008-2009) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Masahiko 奈良女子大学, 人間文化研究科, 教授 (50108974)
SUGAWA Toshiyuki 東北大学, 情報科学研究科, 教授 (30235858)
SAKAN Kenichi 大阪市立大学, 理学研究科, 准教授 (70110856)
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| Co-Investigator(Renkei-kenkyūsha) |
SHIGA Hiroshige 東京工業大学, 理工学研究科, 教授 (10154189)
NAKANISHI Toshihiro 島根大学, 総合理工学研究科, 教授 (00172354)
MIYACHI Hideki 大阪大学, 理学研究科, 准教授 (40385480)
ITO Kentaro 名古屋大学, 多元数理科学研究科, 准教授 (00324400)
FUJIKAWA Ege 千葉大学, 理学研究科, 准教授 (80433788)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 擬対称写像 / 擬等角写像 / メビウス変換群 |
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| Research Abstract |
We define various classes for self-homeomorphisms of the unit circle from a viewpoint of their quasiconformal extension, and study the parameter spaces of those families, which are regarded as Teichmuller spaces. In particular, for the Teichmuller space of symmetric homeomorphisms, we consider conditions for a group acting on this space to have a fixed point in it. As an application, we give a condition for a group of diffeomorphisms to be conjugate to the canonical group action of the circle (Mobius transformations) as well as a condition for the deformation of such a group to be trivial (that is, to have rigidity).
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