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Patterson-Sullivan theory for groups with a strongly contracting element

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arxiv 2206.07361 v6 pith:S6T6BMWR submitted 2022-06-15 math.GR math.DSmath.MG

classification math.GRmath.DSmath.MG
keywords contractingelementgroupspatterson-sullivanstronglyactinggrowthinvestigate
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Using Patterson-Sullivan measures we investigate growth problems for groups acting on a metric space with a strongly contracting element.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Growth gaps and exponential genericity in acylindrically hyperbolic groups

    math.GR 2026-07 conditional novelty 8.0 of 10

    WPD elements are exponentially generic for every finite generating set of an acylindrically hyperbolic group, yielding growth tightness and cogrowth tightness.

  2. Sublinear projection tracking in acylindrically hyperbolic groups

    math.GR 2026-07 accept novelty 8.0 of 10

    For WPD elements, shortest projection in the word metric sublinearly tracks the pullback of shortest projection to the axis in the auxiliary space, yielding effective growth and cocrowth bounds.

  3. Ergodic cocycles in hyperbolic and Hadamard spaces

    math.DS 2025-09 reject novelty 6.0 of 10

    Ergodic cocycles satisfying asymptotic past and future independence converge to the Gromov boundary and have positive drift when integrable.

  4. Sublinear Morse Geodesics and First Passage Percolation

    math.GT 2025-07 conditional novelty 6.0 of 10

    If an infinite bounded-degree graph has a sublinearly Morse bi-infinite quasi-geodesic, then first passage percolation almost surely has a bi-infinite geodesic.

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