Nonlinear spectral gap with respect to non-positively curved spaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17538
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kagoshima University
• Principal Investigator: KONDO Takefumi 鹿児島大学, 理工学域理学系, 准教授 (60467446)
• Project Period (FY): 2015-04-01 – 2018-03-31
• 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

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.

Free Research Field

幾何学