Geometric analysis for non-symmetric generators on Riemannian manifolds
| Project/Area Number |
17K05215
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 熱核 / ポアンカレ定数 / 連結和 / 非対称ランダム・ウォーク / べき零被覆グラフ / 中心極限定理 / 非対称ランダムウォーク / ポアンカレ不等式 |
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| Outline of Final Research Achievements |
In this research project, we investigate geoemtric analysis on a connected sum of non-compact Riemannian manifolds. In particular, we obtain optimal estimates of the long time behavior of the heat kernel and the Poincare constant on manifold with ends. Almostly, the project was done as a joint work with Professor Alexander Grigor'yan from Bielefeld University in Germany and Professor Laurent Saloff-Coste from Cornell University in the US.
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| Academic Significance and Societal Importance of the Research Achievements |
従来、トポロジーなどで使われていた空間の連結和という操作は幾何解析学とは相性が悪く、研究が進んでいなかった。本研究ではこの連結和という解析的には扱いにくい対象上の解析にチャレンジし、適切な仮定のもと、最良の結果を得た。この結果により、例えば結節点のあるような物体の中をランダムに動く粒子や信号がどちらに動きやすいか？という問題についての論理的な根拠を与え、従来よりも効率のよいシステムの開発に貢献することができる。
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Report
(7 results)
Research Products
(28 results)
