Upper bounds for the Steklov eigenvalues on trees

2020/11/22 by Zunwu He, Bobo Hua, He, Zunwu +1 · 7 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2011.11014

openalex publication_date 2020/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, we prove sharp upper bounds for the first nonzero Steklov eigenvalue by the reciprocal of the size of the boundary and the diameter respectively. We also prove similar estimates for higher order Steklov eigenvalues.

Cited by

• Sharp bounds and monotonicity results for Neumann eigenvalues
• The first Steklov eigenvalue bound for graphs of positive genus
• Higher Steklov eigenvalues of graphs on surfaces
• A generalized Cheeger inequality and the Steklov Problem on finite graphs
• Comparison between the first Steklov eigenvalue and algebraic connectivity on trees
• Combinatorial Laplacians and Relative Homology of Complex Pairs
• Random graphs, expanding families and the construction of noncompact hyperbolic surfaces with uniform spectral gaps

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