Structures of manifolds and asymptoticproperties
| Project/Area Number |
22540086
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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 |
Geometry
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | スペクトル逆問題 / 双曲力学系 / 密度定理 / 閉軌道 / 熱核 / 負曲率多様体 / 閉測地線 / 逆問題 / 安定性 / 境界距離 / グロモフハウドルフ距離 |
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| Research Abstract |
We consider stability of geometric spectral inverse problems, which is the problems to get geometric information of manifolds from the eigenvalues and the boundary values of eigenfunctions of the Laplacian on manifolds with boundary, and asymptotic distributions of periods of prime closed orbits on hyperbolic dynamical systems, which are analogy to the prime distribution of the number theory and beyond. Concerning the former problems, we obtain boarder geometric conditions for determination of interior metric from boundary distance function of manifolds with boundary. For the latter case, we get the frame applying the representation theory, perturbation theory, iterated integrals and semi-classical analysis for the Dirichlet density theorem for the Heisenberg extensions.
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Report
(4 results)
Research Products
(11 results)
