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

· 2024 · math.DG · arXiv 2405.19719

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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.

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math.DG 1

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2025 1

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CONDITIONAL 1

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The p-widths of $RP^2$

math.DG · 2025-01-23 · conditional · novelty 6.0

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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  • The p-widths of $RP^2$ math.DG · 2025-01-23 · conditional · none · ref 18 · internal anchor

    The p-widths of (RP^2, g_std) are ω_p = 2π floor((1+sqrt(1+8p))/4), achieved by Z2-invariant polynomial sweepouts.