Higher Steklov eigenvalues of graphs on surfaces
Combinatorics
2026-02-03 v2 Differential Geometry
Functional Analysis
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 with boundary and genus 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).
Cite
@article{arxiv.2511.13472,
title = {Higher Steklov eigenvalues of graphs on surfaces},
author = {Xiongfeng Zhan and Zhe You},
journal= {arXiv preprint arXiv:2511.13472},
year = {2026}
}