We pose the isospectral problem for the p-widths: Is a riemannian manifold (Mⁿ, g) uniquely determined by its p-widths, \ωₚ(M,g)\ₚ₌₁∞? We construct many counterexamples on S² 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) studied this question.
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