2011 Fiscal Year Final Research Report
Geometry of ends, spectrum of Laplacian, scattering, and inverse problem
| Project/Area Number |
21540215
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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 |
Global analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KASUE Atsushi 金沢大学, 理学部, 教授 (40152657)
AKUTAGAWA Kazuo 東北大学, 情報学部, 教授 (80192920)
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| Project Period (FY) |
2009 – 2011
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| Keywords | ラプラス作用素 / スペクトラム / 極限吸収原理 / 絶対連続性 / 平均曲率 / 極小部分多様体 |
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| Research Abstract |
(1) I obtained a sharp criterion of the curvature which shows infinitely many discrete spectrum of the Laplace-Beltrami operator.
(2) I obtained a sharp result which clarifies the relation between the measure growth rate and the absence of embedded eigenvalues of drift Laplacians.
(3) I proved that the limiting absorption principle holds on Riemannian manifolds having ends with various measure growth rates.
(4) I provided the explicitly calculated radii of geodesic balls of a complete noncompact Riemannian submanifold which must exit from the cylindrically bounded domain U, in case its mean curvature is sufficiently small.
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