| Project/Area Number |
12640101
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
UCHIDA Koji Tohoku University, Graduate School of Medicine, Information Sciences, Professor, 大学院・情報科学研究科, 教授 (20004294)
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| Co-Investigator(Kenkyū-buntansha) |
ASOU Tohl Tohoku University, Graduate School of Medicine, Information Sciences, Professor, 大学院・情報科学研究科, 助教授 (00111352)
IMAI Hideo Tohoku University, Graduate School of Medicine, Information Sciences, Assoc. Professor, 大学院・情報科学研究科, 助教授 (10093668)
URAKAWA Hajime Tohoku University, Graduate School of Medicine, Information Sciences, Professor, 大学院・情報科学研究科, 教授 (50022679)
SHIMOKAWA Koya Tohoku University, Graduate School of Medicine, Information Sciences, Assis. Professor, 大学院・情報科学研究科, 助手 (60312633)
TAYA Hisao Tohoku University, Graduate School of Medicine, Information Sciences, Assis. Professor, 大学院・情報科学研究科, 助手 (40257241)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Harmonic morphism of graph / Discrete Laplacian / Inhomogeneous Yang-Mills equation / Einstein-Wey1 geometry / Totally real field / Lambda invariant / Dehn surgery / Heegaard splitting / CR manifold / pseudoharmonic map / Yang-Mills theory / Einstein-Weyl geometry / Greenberg's conjecture / P-class number / Heegaard splitting / Dehn surgery / 無限グラフ / スペクトル / グリーン核 / 熱核 / 岩澤不変量 / Z_P拡大 / Greenberg予想 |
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| Research Abstract |
Urakawa defined the harmonic morphisms of graphs, and gave good estimate of the Green kernel of an infinite tree. He found good estimate of the spectrum of the discrete Laplacian of an infinite graphs. He built Hermitian connections of a vector bundle on a CR manifold, then showed existence and uniqueness of the solution of inhomogeneous Yang-Mills equation. He proved that CR-maps of pseudo convex CR manifolds are pseudoharmonic if and only if they are pseudohermitian. He also introduced the notion of stability of the maps, and proved pseudoharmonic maps into negatively curved Riemannian manifolds are stable. He developed the Yang-Mills theory without the equation Dh=0 for connections in a vector bundle over a Riemannian manifold, and applied this theory to Einstein-Wey1 geometry and to affine differential geometry.
Taya found the formula representing p-class numbers of intermediate fields of the cyclic Zpextension by the values of p-adic zeta functions, assuming Leopoldt conjecture. He also showed there exist infinitely many real quadratic fields in which the prime.3 splits such that lambda invariants are 0. He estimated the density of such fields.
Shimokawa considered Dehn surgeries on strongly invertible knots yielding lens spaces. He found conditions for a graph in the disc to contain some characteristic subgraphs. He showed any Heegaard splitting of trivial arcs in a compression body is standard. He introduced the notion of Heegaard splittings of the pair (M, T), where M is a compact orientable 3-manifold and T is a 1-submanifold.
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