The isospectral problem for $p$-widths: an application of Zoll metrics

Jared Marx-Kuo

doi:10.5802/crmath.708

Article de recherche - Géométrie et Topologie

The isospectral problem for

p

-widths: an application of Zoll metrics
[Le problème isospectral pour les

p

-largeurs : une application des métriques de Zoll]

Jared Marx-Kuo ¹

¹ 450 Jane Stanford Way, Stanford, United States of America

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 565-570.

Abstract (VO)
Résumé

We pose the isospectral problem for the $p$ -widths: is a Riemannian manifold $(M^{n + 1}, g)$ uniquely determined by its $p$ -widths, ${ω_{p} (M, g)}_{p = 1}^{\infty}$ ? We construct many counterexamples on $S^{2}$ using Zoll metrics and the fact that geodesic $p$ -widths are given by unions of immersed geodesics.

Nous posons le problème isospectral pour les $p$ -largeurs : une variété Riemannienne $(M^{n + 1}, g)$ est-elle uniquement déterminée par ses $p$ -largeurs, ${ω_{p} (M, g)}_{p = 1}^{\infty}$ ? Nous construisons de nombreux contre-exemples sur $S^{2}$ en utilisant les métriques de Zoll et le fait que les $p$ -largeurs géodésiques sont données par des unions de géodésiques immergées.

Reçu le : 2024-06-13
Révisé le : 2024-11-19
Accepté le : 2024-12-03
Publié le : 2025-06-05

DOI : 10.5802/crmath.708

Classification : 53C22
Keywords: Min-max,

p

-widths, Zoll, geodesics
Mots-clés : Min-max,

p

-largeurs, Zoll, géodesiques

Affiliations des auteurs :

Jared Marx-Kuo ¹

¹ 450 Jane Stanford Way, Stanford, United States of America

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Jared Marx-Kuo},
     title = {The isospectral problem for $p$-widths: an application of {Zoll} metrics},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {565--570},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.708},
     language = {en},
}

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Jared Marx-Kuo. The isospectral problem for $p$-widths: an application of Zoll metrics. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 565-570. doi : 10.5802/crmath.708. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.708/

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