  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.
