Two counterexamples to a conjecture of Colin de Verdi\`ere on multiplicity
Spectral Theory
2023-12-07 v1 Geometric Topology
Abstract
We exhibit closed hyperbolic surfaces of genus and such that the multiplicity of the first nonzero eigenvalue of their Laplacian is larger than the maximum conjectured by Yves Colin de Verdi\`ere in 1986. In order to determine these multiplicities, we apply the twisted Selberg trace formula to the representations induced by the isometry groups of these surfaces on corresponding triangle groups.
Keywords
Cite
@article{arxiv.2312.03504,
title = {Two counterexamples to a conjecture of Colin de Verdi\`ere on multiplicity},
author = {Maxime Fortier Bourque and Émile Gruda-Mediavilla and Bram Petri and Mathieu Pineault},
journal= {arXiv preprint arXiv:2312.03504},
year = {2023}
}
Comments
20 pages, 3 figures, 3 ancillary files