Triple Products of Eigenfunctions and Spectral Geometry
Spectral Theory
2026-02-20 v4 Mathematical Physics
Functional Analysis
math.MP
Abstract
Using elementary techniques from Geometric Analysis, Partial Differential Equations, and Abelian Algebras, we uncover a novel, yet familiar, global geometric invariant -- namely the indexed set of integrals of triple products of eigenfunctions of the Laplace-Beltrami operator, to precisely characterize which isospectral closed Riemannian manifolds are isometric.
Keywords
Cite
@article{arxiv.2406.12868,
title = {Triple Products of Eigenfunctions and Spectral Geometry},
author = {Joe Schaefer},
journal= {arXiv preprint arXiv:2406.12868},
year = {2026}
}
Comments
8 pages, no figures