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arXiv · 2611.00285

Quantitative spectral rigidity for negatively curved manifolds and Outer Space

Stephen Cantrell
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Abstract

Let $M$ be a closed manifold with fundamental group $G$. A subset of conjugacy classes $E \subset \text{conj}(G)$ 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 $E \subset \text{conj}(G)$, 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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Stephen Cantrell. 2026-10-30. Quantitative spectral rigidity for negatively curved manifolds and Outer Space. https://arxiv.org/abs/2611.00285

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