Nonlinear spectral gap with respect to non-positively curved spaces
| Project/Area Number |
15K17538
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kagoshima University |
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Principal Investigator |
KONDO Takefumi 鹿児島大学, 理工学域理学系, 准教授 (60467446)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 非正曲率空間 / スペクトルギャップ / 正多面体 / 有限コクセター群 / Wirtingerの不等式 / 非線形スペクトルギャップ / 二面体群 / Wirtinger の不等式 / 固定点定理 / アフィン作用 |
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| Outline of Final Research Achievements |
We studied nonlinear spectral gap with respect to non-positively curved spaces, and constructed new examples which exact calculation is possible. Here, nonlinear spectral gap is a quantity defined for a pair of a finite graph and a metric space, which coincides with a spectral gap for Laplacian of a graph when a metric space is a Euclidean space. As applications of Gromov's Wirtinger inequality, we compute nonlinear spectral gap exactly for most of the regular polytopes and for some Coxeter groups and showed that they coincide with the linear case.
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Report
(4 results)
Research Products
(14 results)
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[Presentation] 有限グラフの歪み2017
Author(s)
近藤 剛史
Organizer
第2回摂南大学数理セミナー
Place of Presentation
摂南大学寝屋川キャンパス(大阪府・寝屋川市)
Year and Date
2017-01-21
Related Report
Invited
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