The isospectral problem for $p$-widths: an application of Zoll metrics - Marx-Kuo, Jared (Comptes Rendus. Mathématique)
We pose the isospectral problem for the $p$-widths: is a Riemannian manifold $(M^{n+1}, g)$ uniquely determined by its $p$-widths, $\bigl \lbrace ω _p(M,g)\bigr \rbrace _{p=1}^{∞ }$? We construct many counterexamples on $S^2$ using Zoll metrics and the fact that geodesic $p$-widths are given by unions of immersed geodesics.