New development of inverse spectral problems for singular spaces
| Project/Area Number |
24654010
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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 |
Geometry
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| Research Institution | Kyoto University (2014)
University of Tsukuba (2012-2013) |
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Principal Investigator |
YAMAGUCHI Takao 京都大学, 理学(系)研究科(研究院), 教授 (00182444)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | スペクトル逆問題 / 特異空間 / 熱核 |
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| Outline of Final Research Achievements |
We have obtained the following mathematical findings as results of this reserach project. (1) By a joint work with Ayato Mitsuishi, we found local Lipschitz homotopy structure of Alexandrov spaces.(2) We observed that there is a possibility of establishing Tataru's unique continuation theorem for waves on the GH-limit spaces of Riemannian manifolds whose Ricci curvatures are uniformly bounded below. (3)We found that considering spectral limits of Schrodinger operators on collapsed surfaces whose curvatures explode to -infinity should be usuful in the study of waves of some quantum graphs.
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Report
(4 results)
Research Products
(9 results)
