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arXiv · 2405.19719

The Isospectral Problem for p-widths: An Application of Zoll Metrics

Jared Marx-Kuo
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Abstract

We pose the isospectral problem for the $p$-widths: Is a riemannian manifold $(M^n, g)$ uniquely determined by its $p$-widths, $\{ω_p(M,g)\}_{p=1}^{\infty}$? We construct many counterexamples on $S^2$ using Zoll metrics and the fact that geodesic $p$-widths are given by unions of immersed geodesics.

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Jared Marx-Kuo. 2024-05-30. The Isospectral Problem for p-widths: An Application of Zoll Metrics. https://arxiv.org/abs/2405.19719

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