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Marked length spectrum rigidity from rigidity on subsets

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arxiv 2304.13209 v2 pith:LVN2LL4D submitted 2023-04-26 math.GT math.GR

Stephen Cantrell , Eduardo Reyes This is my paper
classification math.GTmath.GR
keywords lengthrigidityspectrumgeometricmarkedresultsstudyingable
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We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like functions coming from various geometric origins. Using our new perspective, we provide concise proofs of well-known length spectrum rigidity results and are able to extend classical results to a variety of new settings. Our methods rely on studying Manhattan curves and a coarse geometric analogue of Teichm\"uller space equipped with a symmetrized version of the Thurston metric.

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Cited by 1 Pith paper

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  1. Volume Entropy Rigidity for Random Groups at Low Densities

    math.GR 2025-05 accept novelty 7.0 of 10

    Generic random groups at extremely low density have a unique entropy-minimizing normalized weight, which is nearly uniform.

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