| Project/Area Number |
23654061
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Gakushuin University (2013)
Tohoku University (2011-2012) |
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Principal Investigator |
YAMADA Sumio 学習院大学, 理学部, 教授 (90396416)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Makoto 山形大学, 理学部, 教授 (70312634)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | アインシュタイン方程式 / 発展方程式 / 極小曲面 / リーマン計量 / コーシー初期条件 / リーマン計量の変形理論 / 共形幾何 / ハミルトン力学系 / 国際研究者交流（アメリカ） / 国際研究者交流（オーストラリア） / 国際情報交換（アメリカ） / 国際情報交換（中国） |
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| Research Abstract |
Based on ideas inherent in two major advances in the field of geometric analysis, namely, Perelman's resolution of Ricci flow, and Bray's proof of Riemannian Penrose inequality using conformal deformation of Riemannian metrics, the PI has succeeded in generalizing the Penrose inequality, concerning the solution of the Einstein-Maxwell equation. The Investigator Nakamura has also obtained a set of interesting results in the field of nonlinear hyperbolic partial differential equations, which are closely related to the Einstein equation.
Under the support of the current grant, two international meetings were organized in Japan, and together with attending academic meetings abroad, the investigators Yamada and Nakamura established opportunities for exchanges of ideas, which led to the collaboration with Gilbert Weinstein and Marcus Khuri, which in turn became the major work described above.
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