Geometry of ends, spectrum of Laplacian, scattering, and inverse problem
Project/Area Number |
21540215
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Global analysis
|
Research Institution | Shizuoka University |
Principal Investigator |
|
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)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
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 / ラプラス-ベルトラミ作用素 / 固有値の非存在 / リーマン部分多様体 / ノン・コンパクト・リーマン多様体 / ラプラス・ベルトラミ作用素 / スペクトル / エンド / 放射曲率 / ラプラシアン |
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.
|
Report
(4 results)
Research Products
(15 results)