| Project/Area Number |
24340008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology (2013-2017)
Tohoku University (2012) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
FUTAKI Akito 東京大学, 数理科学研究科, 教授 (90143247)
KOBAYASHI Osamu 大阪市立大学, 数学研究所, 特別研究員 (10153595)
FURUTA Mikio 東京大学, 数理科学研究科, 教授 (50181459)
NAYATANI Shin 名古屋大学, 多元数理科学研究科, 教授 (70222180)
ONO Hajime 埼玉大学, 理工学部, 准教授 (70467033)
HONDA Shouhei 東北大学, 理学研究科, 准教授 (60574738)
MATSUO Shinichiroh 名古屋大学, 多元数理科学研究科, 准教授 (40599487)
MATSUMOTO Yoshihiko 大阪大学, 理学研究科, 助教 (00710625)
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| Research Collaborator |
Carron Gilles Université de Nantes, Département de Mathématiques, Professor
Mazzeo Rafe Stanford University, Department of Mathematics, Professor
Mondello Ilaria Université de Nantes, Département de Mathématiques, Researcher
Vertman Boris Universität Münster, Mathematisches Institut, Professor
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| Project Period (FY) |
2012-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥17,810,000 (Direct Cost: ¥13,700,000、Indirect Cost: ¥4,110,000)
Fiscal Year 2016: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | 微分幾何 / 幾何解析 / スカラー曲率 / アインシュタイン計量 / 山辺不変量 / 国際研究交流 / 国際情報交換 / 多国籍 |
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| Outline of Final Research Achievements |
On a compact manifold with very general singularities, we have studied the Yamabe problem and have established a generalization of Aubin’s inequality for Yamabe constants. When the inequality is strict, we have proved the existence of singular Yamabe metrics.
When the equality of the inequality holds, we have constructed an example of singular manifolds which have not singular Yamabe metrics. For an edge-cone Einstein metric on a smooth manifold, we have constructed an appropriate family of smooth metrics with Ricci curvature bounded below by the Einstein constant. As a corollary, we have obtained an estimate of the Yamabe invariant from below by using the existence of edge-cone Einstein metrics.
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