Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915966103846912 |
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| author | Erchenko, Alena Jakobson, Dmitry Tsypin, Allison |
| author_facet | Erchenko, Alena Jakobson, Dmitry Tsypin, Allison |
| contents | It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular space can be well approximated by the eigenvalues of the discrete Laplacian on a certain graph coming from the pair of pants decomposition of the surface. In this paper, we provide a complete description of the sets of eigenvalues of the weighted graph Laplacian for all graphs on four vertices that correspond to a valid pair of pants decomposition of a surface of genus 3. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26308 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces Erchenko, Alena Jakobson, Dmitry Tsypin, Allison Spectral Theory Differential Geometry Primary 05C50, 58J50, Secondary 05C22, 05C90, 58C40, 52A55 It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular space can be well approximated by the eigenvalues of the discrete Laplacian on a certain graph coming from the pair of pants decomposition of the surface. In this paper, we provide a complete description of the sets of eigenvalues of the weighted graph Laplacian for all graphs on four vertices that correspond to a valid pair of pants decomposition of a surface of genus 3. |
| title | Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces |
| topic | Spectral Theory Differential Geometry Primary 05C50, 58J50, Secondary 05C22, 05C90, 58C40, 52A55 |
| url | https://arxiv.org/abs/2604.26308 |