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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13472 |
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| _version_ | 1866908804238540800 |
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| author | Zhan, Xiongfeng You, Zhe |
| author_facet | Zhan, Xiongfeng You, Zhe |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Steklov eigenvalues of graphs on surfaces Zhan, Xiongfeng You, Zhe Combinatorics Differential Geometry Functional Analysis 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). |
| title | Higher Steklov eigenvalues of graphs on surfaces |
| topic | Combinatorics Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2511.13472 |