Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces
Spectral Theory
2026-04-30 v1 Differential Geometry
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.
Cite
@article{arxiv.2604.26308,
title = {Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces},
author = {Alena Erchenko and Dmitry Jakobson and Allison Tsypin},
journal= {arXiv preprint arXiv:2604.26308},
year = {2026}
}
Comments
20 pages, 2 figures