Sparse spectrally rigid sets for negatively curved manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918046502748160 |
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| author | Cantrell, Stephen |
| author_facet | Cantrell, Stephen |
| contents | Suppose that $(M,\mathfrak{g})$ is a compact Riemannian manifold with strictly negative sectional curvatures. A subset of conjugacy classes $E \subset \text{conj}(π_1(M))$ is called spectrally rigid if when two negatively curved Riemannian metrics $\mathfrak{g}_1, \mathfrak{g}_2$ on $M$ have the same marked length spectrum on $E$, then their marked length spectra coincide everywhere. In this work we show that there are arbitrarily sparse spectrally rigid sets and that they exist, in some sense, in every direction in $π_1(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16545 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sparse spectrally rigid sets for negatively curved manifolds Cantrell, Stephen Dynamical Systems Differential Geometry Geometric Topology Suppose that $(M,\mathfrak{g})$ is a compact Riemannian manifold with strictly negative sectional curvatures. A subset of conjugacy classes $E \subset \text{conj}(π_1(M))$ is called spectrally rigid if when two negatively curved Riemannian metrics $\mathfrak{g}_1, \mathfrak{g}_2$ on $M$ have the same marked length spectrum on $E$, then their marked length spectra coincide everywhere. In this work we show that there are arbitrarily sparse spectrally rigid sets and that they exist, in some sense, in every direction in $π_1(M)$. |
| title | Sparse spectrally rigid sets for negatively curved manifolds |
| topic | Dynamical Systems Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2310.16545 |