Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs

2020/10/27 by Yongjie Shi, Shi, Yongjie, Chengjie Yu +1 · 4 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Graph theory and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2010.13969

openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity. As applications of the comparison of eigenvalues, we obtain Lichnerowicz-type estimates and some combinatorial estimates for Steklov eigenvalues on graphs.

Cited by

• Sharp bounds and monotonicity results for Neumann eigenvalues
• A generalized Cheeger inequality and the Steklov Problem on finite graphs
• Comparison between the first Steklov eigenvalue and algebraic connectivity on trees
• Random graphs, expanding families and the construction of noncompact hyperbolic surfaces with uniform spectral gaps

Related

• A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity
• Comparisons of Dirichlet, Neumann and Laplacian eigenvalues on graphs and their applications
• Monotonicity of Steklov eigenvalues on graphs and applications
• Extension and rigidity of Perrin's lower bound estimate for Steklov eigenvalues on graphs
• Minimal Steklov eigenvalues on combinatorial graphs