| Project/Area Number |
13440051
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
URAKAWA Hajime Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (50022679)
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| Co-Investigator(Kenkyū-buntansha) |
ARISAWA Mariko Tohoku University, Graduate School of Information Sciences, Associate Professor, 大学院・情報科学研究科, 助教授 (50312632)
KANEKO Makoto Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (10007172)
ASOH Tohl Tohoku University, Graduate School of Information Sciences, Associate Professor, 大学院・情報科学研究科, 助教授 (00111352)
OBATA Nobuaki Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (10169360)
OHNO Yoshiki Tohoku University, Graduate School of Information Sciences, Associate Professor, 大学院・情報科学研究科, 助教授 (80005777)
内田 興二 東北大学, 大学院・情報科学研究科, 教授 (20004294)
伊藤 仁一 熊本大学, 教育学部, 助教授 (20193493)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥14,700,000 (Direct Cost: ¥14,700,000)
Fiscal Year 2003: ¥4,700,000 (Direct Cost: ¥4,700,000)
Fiscal Year 2002: ¥4,500,000 (Direct Cost: ¥4,500,000)
Fiscal Year 2001: ¥5,500,000 (Direct Cost: ¥5,500,000)
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| Keywords | Yang-Mills connection / Dirichlet eigenvalue problem / finite element method / infinite graph / affine connection / oseudharmonic map / Green kernel / symplectic manifold / ヤング・ミズル接続 / ワイル接続 / モデュライ空間 / チーガー定数 / 熱核 / 鋭角三角形分割 / 境界値問題 / 固有値 / 離散計算幾何 / 非退化CR多様体 / 擬エネルギー汎関数 / 共役接続 / ヤングミルズ接続 |
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| Research Abstract |
We have obtained the following results:
(1)We constructed the theory of Yang-Mills connections over compact symplectic manifolds.
(2)We estimated the Cheeger constant, the heat kernel and the Green kernel for an infinite graph in terms of the volume growth, growth of in and out degree.
(3)We determined the stiffness and mass matrices of the finite element method for the Dirichlet eigenvalue problem for a plane domain.
(4)We calculated the Cheeger constant, the heat kernel and Green kernel of semi-regular infinite graphs and gave the explicit comparison theorem for every infinite graph.
(5)We extended Yang-Mills theory to Weyl structure, and established Atiya-Hitchin-Singer theory to Weyl manifolds, and to affine connections.
(6)We formulated discrete improper affine surface theory and show its loop group description.
(7)We showed the relation in affine differential geometry, Weyl geometry, Yang-Mills theory.
(8)We defined the notion of pseudoharmonic maps from CR manifolds to a Riemanninan manifold, and showed the first variation formula and the second variation formula.
(9)We clarified the relation of each Yang-Mills theory on Kaehler manifolds, CR manifolds, and symplectic manifolds, and characterized the minimizers of the Yang-Mills functional over compact symplectic manifolds.
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