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Marked length spectrum rigidity for relatively hyperbolic groups

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arxiv 2207.05296 v1 pith:4WDLDBCJ submitted 2022-07-12 math.GT math.GRmath.MG

Thang Nguyen , Shi Wang This is my paper · ORCID
classification math.GTmath.GRmath.MG
keywords lengthmarkedmetricsrigidityspectrumgroupshyperbolicrelatively
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We consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function) under the two metrics are the same, then the two metrics are uniformly close. We prove the rigidity theorem for relatively hyperbolic groups. This generalizes a result of Fujiwara.

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Cited by 1 Pith paper

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  1. Stability for boundary actions of cocompact lattices in Euclidean buildings

    math.DS 2026-07 accept novelty 7.0 of 10

    Cocompact lattice actions on flag boundaries of Euclidean buildings are topologically stable: every sufficiently small perturbation is semi-conjugate to the original action.

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