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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.09019 |
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| _version_ | 1866917622041280512 |
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| author | Hao, Yanlong |
| author_facet | Hao, Yanlong |
| contents | Let $(X,d)$, $(Y, d')$ be two roughly geodesically complete Gromov hyperbolic spaces under comparable isometric actions of $Γ$. Assume that the limit set $ΛΓ=\partial X\partial Y$. If spaces $X$ and $Y$ have the same asymptotic marked length spectrum, meaning that
$$\lim_{{l_{d}([γ])\to \infty}}\frac{l_d(γ)}{l_{d'}(γ)}=1.$$ Then $(X,d)$ and $(Y,d')$ are $Γ$-equivariantly roughly isometric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Marked length spectra of Gromov hyperbolic space Hao, Yanlong Geometric Topology Group Theory 37D40, 37A20 Let $(X,d)$, $(Y, d')$ be two roughly geodesically complete Gromov hyperbolic spaces under comparable isometric actions of $Γ$. Assume that the limit set $ΛΓ=\partial X\partial Y$. If spaces $X$ and $Y$ have the same asymptotic marked length spectrum, meaning that $$\lim_{{l_{d}([γ])\to \infty}}\frac{l_d(γ)}{l_{d'}(γ)}=1.$$ Then $(X,d)$ and $(Y,d')$ are $Γ$-equivariantly roughly isometric. |
| title | Marked length spectra of Gromov hyperbolic space |
| topic | Geometric Topology Group Theory 37D40, 37A20 |
| url | https://arxiv.org/abs/2312.09019 |