Marked Length Spectrum Rigidity for Surface Amalgams
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915051772837888 |
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| author | Wu, Yandi |
| author_facet | Wu, Yandi |
| contents | In this paper, we show that simple, thick negatively curved two-dimensional P-manifolds, a large class of surface amalgams, are marked length spectrum rigid. That is, if two piecewise negatively curved Riemannian metrics (satisfying certain smoothness conditions) on a simple, thick two-dimensional P-manifold assign the same lengths to all closed geodesics, then they differ by an isometry up to isotopy. Our main theorem is a natural generalization of Croke and Otal's celebrated results about marked length spectrum rigidity of negatively curved surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09968 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Marked Length Spectrum Rigidity for Surface Amalgams Wu, Yandi Geometric Topology Dynamical Systems Group Theory 57M50, 53C24, 37D40 In this paper, we show that simple, thick negatively curved two-dimensional P-manifolds, a large class of surface amalgams, are marked length spectrum rigid. That is, if two piecewise negatively curved Riemannian metrics (satisfying certain smoothness conditions) on a simple, thick two-dimensional P-manifold assign the same lengths to all closed geodesics, then they differ by an isometry up to isotopy. Our main theorem is a natural generalization of Croke and Otal's celebrated results about marked length spectrum rigidity of negatively curved surfaces. |
| title | Marked Length Spectrum Rigidity for Surface Amalgams |
| topic | Geometric Topology Dynamical Systems Group Theory 57M50, 53C24, 37D40 |
| url | https://arxiv.org/abs/2310.09968 |