• Corpus ID: 244798743

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… 

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