# Tent property and directional limit sets for self-joinings of hyperbolic manifolds

@inproceedings{Kim2021TentPA, title={Tent property and directional limit sets for self-joinings of hyperbolic manifolds}, author={Dongryul Kim and Yair N. Minsky and Hee Oh}, year={2021} }

. (1) Let Γ = ( ρ 1 × ρ 2 )(∆) where ρ 1 , ρ 2 : ∆ → SO ◦ ( n, 1) are convex cocompact representations of a finitely generated group ∆. We provide a sharp pointwise bound on the growth indicator function ψ Γ by a tent function: for any v = ( v 1 , v 2 ) ∈ R 2 , ψ Γ ( v ) ≤ min( 1 dim H Λ 1 2 H Λ 2 ) . We obtain several interesting consequences including the gap and rigidity property on the critical exponent. (2) Generalizing this, we propose a conjecture that ψ Γ is at most the half sum of all…

## 9 Citations

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. Let G be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup Γ < G , we show that a Γ-conformal measure is supported on the limit set of Γ if and only if its dimension…

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. Let G = SO ◦ ( n, 1) × SO ◦ ( n, 1) and X = H n × H n for n ≥ 2. For a pair ( π 1 , π 2 ) of non-elementary convex cocompact representations of a ﬁnitely generated group Σ into SO ◦ ( n, 1), let Γ…

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### TEMPEREDNESS OF L2(Γ\G) AND POSITIVE HARMONIC FUNCTIONS IN HIGHER RANK

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Let G = SO◦(n, 1)×SO◦(n, 1) and X = H×H for n ≥ 2. For a pair (π1, π2) of non-elementary convex cocompact representations of a finitely generated group Σ into SO◦(n, 1), let Γ = (π1×π2)(Σ). We show:…

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Let G = SO(n1, 1) × SO(n2, 1) and X = H1 × H2 for n1, n2 ≥ 2. Let Γ = (π1×π2)(Σ) where πi : Σ→ Gi is a non-elementary convex cocompact representation of a finitely generated group Σ. We show: (1)…

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### TEMPEREDNESS OF L2(Γ\G) AND POSITIVE HARMONIC FUNCTIONS IN HIGHER RANK

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Let G = SO◦(n, 1)×SO◦(n, 1) and X = H×H for n ≥ 2. For a pair (π1, π2) of non-elementary convex cocompact representations of a finitely generated group Σ into SO◦(n, 1), let Γ = (π1×π2)(Σ). We show:…

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