Monotonicity of Steklov eigenvalues on graphs and applications

2021/12/24 by Chengjie Yu, Yu, Chengjie, Yingtao Yu +1 · 4 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Combinatorics (math.CO) #Differential Equations and Numerical Methods #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2112.12885

openalex publication_date 2021/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain monotonicity of Steklov eigenvalues on graphs which as a special case on trees extends the results of He-Hua [Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 101, arXiv: 2103.07696] to higher Steklov eigenvalues and gives affirmative answers to two problems proposed in He-Hua [arXiv: 2103.07696]. As applications of the monotonicity of Steklov eigenvalues, we obtain some estimates for Steklov eigenvalues on trees generalizing the isodiametric estimate for the first positive Steklov eigenvalues on trees in He-Hua [arXiv:2011.11014].

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• Sharp bounds and monotonicity results for Neumann eigenvalues
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• Comparison between the first Steklov eigenvalue and algebraic connectivity on trees

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