| Project/Area Number |
26800057
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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 | Shizuoka University (2017)
Tokyo University of Science (2015-2016)
Nagoya University (2014) |
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Principal Investigator |
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| Research Collaborator |
Brinkschulte Judith Universität Leipzig, Mathematisches Institut, Wissenschaftlicher Mitarbeiter
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | レビ平坦曲面 / 複素解析幾何 / 多変数関数論 / 葉層構造論 / 微分幾何学 / ポテンシャル論 / エルゴード理論 / 国際情報交換 / モンジュアンペール方程式 / 超幾何関数 / ハーディー空間 / モンジュ・アンペール測度 / 多重劣調和関数 / 曲率 |
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| Outline of Final Research Achievements |
This research project focused on Levi-flats, manifolds foliated by complex manifolds. Combining ideas from complex analysis, theory of dynamical system, and differential geometry, we obtained following results: We improved known curvature restrictions for hypothetical Levi-flats in complex projective planes. We proved an inequality for the Diederich-Fornaess index on abstract Levi-flats. We gave potential theoretic proof for non-existence of bounded holomorphic functions on bi-disk invariant by the diagonal action of Fuchsian groups without relying on ergodicity theorems, and also found an explicit construction for such invariant holomorphic functions by means of integral transformations.
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