The Isospectral Problem for p-widths: An Application of Zoll Metrics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913370211352576 |
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| author | Marx-Kuo, Jared |
| author_facet | Marx-Kuo, Jared |
| contents | We pose the isospectral problem for the $p$-widths: Is a riemannian manifold $(M^n, g)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19719 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Isospectral Problem for p-widths: An Application of Zoll Metrics Marx-Kuo, Jared Differential Geometry We pose the isospectral problem for the $p$-widths: Is a riemannian manifold $(M^n, g)$ 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. |
| title | The Isospectral Problem for p-widths: An Application of Zoll Metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.19719 |