Marked length spectra of Gromov hyperbolic space

2023/12/14 by Hao, Yanlong
#37A20 #37D40 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.09019

Abstract

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=∂ X∂ Y. If spaces X and Y have the same asymptotic marked length spectrum, meaning that lim_l_d([γ])→ ∞\fracl_d(γ)l_d'(γ)=1. Then (X,d) and (Y,d') are Γ-equivariantly roughly isometric.

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