2013 Fiscal Year Final Research Report
Research on the complex structure on Teichmuller space and the deformation space of Kleinian groups
| Project/Area Number |
21540177
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Osaka University |
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Principal Investigator |
HIDEKI Miyachi 大阪大学, 理学(系)研究科(研究院), 准教授 (40385480)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | タイヒミュラー空間 / モジュライ空間 / タイヒミュラー距離 / 極値的長さ / 写像類群 / ホロ関数境界 / グロモフ積 |
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| Research Abstract |
In this period, I study the geometry of Teichmuller space. I obtain the intersection number in extremal length geometry of Teichmuller space. As applications, we have an alternative proofs of Royden-Earle-Kra-Markovic-Ivanov's result ``Except for few cases, the isometry group on Teichmuller space coincides with the extended mapping class group", and Masur-Wolf's theorem ``Teichmuller space is not Gromov-hyperbolic". I also obtain a rigidity theorem of holomorphic disks in Teichmuller space by using the asymptotic behavior of the Gromov product. This is an application of our Thurston theory to the study of the complex structure on Teichmuller space.
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