| Project/Area Number |
15K04914
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka City University (2016-2018)
Fukushima University (2015) |
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Principal Investigator |
Hamano Sachiko 大阪市立大学, 大学院理学研究科, 准教授 (10469588)
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| Co-Investigator(Kenkyū-buntansha) |
柴 雅和 広島大学, 工学研究科, 名誉教授 (70025469)
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| Research Collaborator |
YAMAGUCHI hiroshi
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 解析学 / 複素解析 / 多変数関数論 / 擬凸領域 / 多重劣調和関数 / スタイン多様体 / 多重劣調和 |
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| Outline of Final Research Achievements |
We showed log-plurisubharmonicity of metric deformations induced by Schiffer and harmonic spans if the total space is a two-dimensional Stein manifold such that each fiber is a planar open Riemann surface. As an application, we proved that both metrics in fact coincide on planar open Riemann surfaces, have negative curvature everywhere, and are complete.
Moreover, in the case of genus one, we studied the variation of hyperbolic spans of open Riemann surfaces. We proved that the hyperbolic span is subharmonic if the total space is a two-dimensional Stein manifold such that each fiber is an open Riemann surface of genus one. In particular, the hyperbolic span is harmonic if and only if the total space is a trivial holomorphic family.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の目的は、2次元擬凸領域をそこで定義された正則関数の定数面/ファイバーの族として捉えたとき、ファイバー上に全空間の擬凸性を反映する良いモジュライを新たに構成することで、2次元擬凸領域のモジュライ理論を展開することである。特に、一変数関数論における多重連結領域の等角写像およびポテンシャル論における各主関数のディリクレ問題・ノイマン問題、2乗可積分な半完全正則微分のなす空間の再生核、および多変数関数論的変動である擬凸性との関係を明らかにすることで、全空間の擬凸性を反映する種々の等角不変量の変動の解析へと進化させた。
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