PreprintCC BY 4.0arXiv
Quantitative spectral rigidity for negatively curved manifolds and Outer Space
Abstract
Let M be a closed manifold with fundamental group G. A subset of conjugacy classes E ⊂ conj(G) is said to be spectrally rigid if when two negatively curved Riemannian metrics have the same marked length spectra on E, then their length spectra agree on all conjugacy classes. In this work we study spectrally rigid subsets from a quantitative perspective. We show that, if the density of E ⊂ conj(G), measured with respect to a fixed reference metric, decays more slowly than T−1/2 then E is spectrally rigid. We establish analogous rigidity results for Culler-Vogtmann Outer Space and show that the T−1/2 threshold is sharp in this setting.
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BibTeX
@misc{cantrell2026quantitative,
title = {{Quantitative spectral rigidity for negatively curved manifolds and Outer Space}},
author = {Stephen Cantrell},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00285},
eprint = {2611.00285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00285},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantitative spectral rigidity for negatively curved manifolds and Outer Space
AU - Stephen Cantrell
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00285
UR - https://arxiv.org/abs/2611.00285
AB - Let M be a closed manifold with fundamental group G. A subset of conjugacy classes E ⊂ conj(G) is said to be spectrally rigid if when two negatively curved Riemannian metrics have the same marked length spectra on E, then their length spectra agree on all conjugacy classes. In this work we study spectrally rigid subsets from a quantitative perspective. We show that, if the density of E ⊂ conj(G), measured with respect to a fixed reference metric, decays more slowly than T^−1/2 then E is spectrally rigid. We establish analogous rigidity results for Culler-Vogtmann Outer Space and show that the T^−1/2 threshold is sharp in this setting.
ER -