Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces

Alena Erchenko; Dmitry Jakobson; Allison Tsypin

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arXiv · 2604.26308

Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces

Alena Erchenko·Dmitry Jakobson·Allison Tsypin

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Abstract

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.

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Alena Erchenko, Dmitry Jakobson, Allison Tsypin. 2026-04-29. Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces. https://arxiv.org/abs/2604.26308

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