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arXiv · 2511.13472

Higher Steklov eigenvalues of graphs on surfaces

Xiongfeng Zhan·Zhe You
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Abstract

In this paper, we study the higher Steklov eigenvalues of graphs on surfaces. We obtain the upper bound of higher Steklov eigenvalues of a finite graph $G$ with boundary $B$ and genus $g$ by using metrical deformation via probability flows. Our result can be regarded as a discrete analogue of Karpukhin's bound in spectral geometry. Moreover, this result implies the upper bound of higher Laplacian eigenvalues given by Kelner, Lee, Price and Teng (Geom. Funct. Anal., 2011).

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Xiongfeng Zhan, Zhe You. 2026-02-02. Higher Steklov eigenvalues of graphs on surfaces. https://arxiv.org/abs/2511.13472

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