2013 Fiscal Year Final Research Report
New development of the theory of infinite dimensional Teichmuller spaces: construction of moduli spaces
| Project/Area Number |
23740102
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Chiba University |
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Principal Investigator |
FUJIKAWA Ege 千葉大学, 理学(系)研究科(研究院), 准教授 (80433788)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 複素解析学 / リーマン面 / 擬等角写像 / タイヒミュラー空間 / 写像類群 / モジュライ空間 / 双曲幾何学 |
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| Research Abstract |
On the classification of the Teichmuller modular transformations in infinite dimensional Teichmuller spaces, we investigated properties of transformations of infinite discrete type and those of divergent type. We also observed asymptotic Teichmuller modular transformations acting on asymptotic Teichmuller spaces and obtained a sufficient condition to be of finite order. Furthermore, for a subgroup of the quasiconformal mapping class group that is stationary, we observed discontinuity of the action on the space of asymptotically conformal classes.
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