PreprintCC BY 4.0arXiv
Regular hyperbolic tilings have no ℓ2 eigenfunctions
Abstract
We show that the adjacency operator of the $1$-skeleton of any regular tiling of the hyperbolic plane has no nonzero square-integrable eigenfunctions. As a consequence, the same holds for every infinite connected regular graph admitting a proper planar embedding with regular dual.
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BibTeX
@misc{nachmias2026regular,
title = {{Regular hyperbolic tilings have no $\ell^2$ eigenfunctions}},
author = {Asaf Nachmias},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11857},
eprint = {2609.11857},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11857},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regular hyperbolic tilings have no ℓ^2 eigenfunctions
AU - Asaf Nachmias
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11857
UR - https://arxiv.org/abs/2609.11857
AB - We show that the adjacency operator of the $1$-skeleton of any regular tiling of the hyperbolic plane has no nonzero square-integrable eigenfunctions. As a consequence, the same holds for every infinite connected regular graph admitting a proper planar embedding with regular dual.
ER -