An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs

zbMath1439.05074arXiv1712.03465MaRDI QIDQ2176722

Taiki Yamada

Publication date: 5 May 2020

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03465

zbMATH Keywords

Laplacians on simplicial complexes

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Global Riemannian geometry, including pinching (53C20) Distance in graphs (05C12) Discrete geometry (52C99)

Cites Work

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• Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
• Ricci curvature of graphs
• Ricci curvature of Markov chains on metric spaces
• Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
• Ricci curvature and eigenvalue estimate on locally finite graphs
• Spectra of combinatorial Laplace operators on simplicial complexes
• Harmonic functions and boundary value problems on a chain complex
• Optimal Transport

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