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Main Author: Hao, Yanlong
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2312.09019
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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