Compactification of Riemannian manifolds and embeddings of graphs
Project/Area Number |
24540072
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Kanazawa University |
Principal Investigator |
Kasue Atsushi 金沢大学, 数物科学系, 教授 (40152657)
|
Co-Investigator(Kenkyū-buntansha) |
Hattori Tae 石川工業高等専門学校, 一般教育, 講師 (40569365)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | リーマン多様体 / ネットワーク / 理想境界 / ディリクレ形式 / ディリクレエネルギー有限写像 / ランダムウォーク / スペクトルギャップ / 双曲埋め込み / ディクレエネルギー有限写像 / 無限ネットワーク / 有効抵抗 / 容量 / 倉持コンパクト化 / p-調和関数 / p-ディリクレ和有限関数 / 測地的コンパクト化 |
Outline of Final Research Achievements |
We study a connected nonparabolic, or transient network compactified with the Kuramochi boundary, and show that the random walk converges almost surely to a random variable valued in the harmonic boundary, and a function of finite Dirichlet energy converges along the random walk to a random variable almost surely and in L2. We also give integral representations of solutions of Poisson equations on the Kuramochi compactification. We also study finite connected graphs which admit quasi monomorphisms to hyperbolic spaces and give geometric bounds for the Cheeger constants in terms of the volume, an upper bound of the degree, and the quasi monomorphism. Moreover we develop a potential theory of nonlinear networks in the frame work of modular sequence spaces.
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Report
(5 results)
Research Products
(5 results)