PreprintarXiv licencearXiv
Generic properties of the Laplace spectrum and eigenfunctions
Abstract
We prove that the spectrum of the Laplace--Beltrami operator on compact Riemannian manifolds without boundary is generically linearly independent over ℚ. Furthermore, we prove that pointwise products of eigenfunctions generically are linearly independent. The proof is based on conformal perturbations of the metric. The result implies in particular that generically the truncation of the continuous functions on M by spectral projections of the Laplace operator is given by symmetric matrices.
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BibTeX
@misc{furst2026generic,
title = {{Generic properties of the Laplace spectrum and eigenfunctions}},
author = {Oliver Fürst and Eva-Maria Hekkelman and Malte Leimbach},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40859},
eprint = {2610.40859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40859},
}
RIS
TY - UNPB
TI - Generic properties of the Laplace spectrum and eigenfunctions
AU - Oliver Fürst
AU - Eva-Maria Hekkelman
AU - Malte Leimbach
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40859
UR - https://arxiv.org/abs/2610.40859
AB - We prove that the spectrum of the Laplace--Beltrami operator on compact Riemannian manifolds without boundary is generically linearly independent over ℚ. Furthermore, we prove that pointwise products of eigenfunctions generically are linearly independent. The proof is based on conformal perturbations of the metric. The result implies in particular that generically the truncation of the continuous functions on M by spectral projections of the Laplace operator is given by symmetric matrices.
ER -