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The Isospectral Problem for p-widths: An Application of Zoll Metrics
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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, $\{\omega_p(M,g)\}_{p=1}^{\infty}$? We construct many counterexamples on $S^2$ using Zoll metrics and the fact that geodesic $p$-widths are given by unions of immersed geodesics.
Forward citations
Cited by 2 Pith papers
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On Zoll Contact 5-Spheres
Every Zoll contact form on the standard contact 5-sphere is strictly contactomorphic to a scaling of the standard Zoll form.
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The p-widths of $RP^2$
The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.
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