2015 Fiscal Year Final Research Report
Resolution of conjugation problems on circle diffeomorphism groups
| Project/Area Number |
24654035
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TANIGUCHI MASAHIKO 奈良女子大学, 自然科学系, 教授 (50108974)
FUJIKAWA EGE 千葉大学, 理学研究科, 准教授 (80433788)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 複素解析学 / 微分幾何学 |
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| Outline of Final Research Achievements |
(1) We introduced the Teichmueller space of circle diffeomorphisms with Hoelder continuous derivatives and established its foundation. (2) We proved that if a group of Moebius transformations is conjugate to a group of circle diffeomorphisms with Hoelder continuous derivatives by a symmetric homeomorphism, then the conjugating map actually has a Hoelder continuous derivative of the same order. (3) We obtained a necessary and sufficient condition for a group of circle diffeomorphisms with α-Hoelder continuous derivatives for α>1/2 to be conjugate to a group of Moebius transformations by a circle diffeomorphism with an α-Hoelder continuous derivative in terms of uniform integrability of the complex dilatations of quasiconformal extensions of the group elements. (4) Even if we do not assume α>1/2, we showed that if the integrability of quasiconformal extensions is uniformly bounded by a certain constant sufficiently small, then the above result still holds true.
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| Free Research Field |
タイヒミュラー空間論
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