| 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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| 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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