Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tent property and directional limit sets for self-joinings of hyperbolic
  manifolds   Let $\Gamma=(\rho_1\times \rho_2)(\Delta)$ where $\rho_1,\rho_2:\Delta\to
\operatorname{SO}^\circ(n,1)$ are convex cocompact representations of a
finitely generated group $\Delta$.
  (1): We provide a sharp pointwise bound on the growth indicator function
$\psi_\Gamma$ by a tent function: for any $v=(v_1, v_2)\in {\mathbb R}^2$: $$
\psi_\Gamma(v)\le \min (v_1 \operatorname{dim}_{\operatorname{H}}
\Lambda_{\rho_1}, v_2 \operatorname{dim}_{\operatorname{H}}
\Lambda_{\rho_2}).$$ We obtain several interesting consequences including the
gap and rigidity property on the critical exponent.
  (2): Generalizing this, we propose a conjecture that $\psi_\Gamma$ is at most
the half sum of all positive roots for any Anosov subgroup of a semisimple real
algebgraic group of rank at least $2$. We confirm this conjecture for Zariski
dense Anosov subgroups of Hitchin groups.
  (3): For each $v$ in the interior of the limit cone of $\Gamma$, we prove the
following on the $v$-directional conical limit set $\Lambda_v\subset \mathbb
S^{n-1}\times \mathbb S^{n-1}$: $$ \tfrac{\psi_\Gamma(v)}{\max{(v_1, v_2)} }\le
\operatorname{dim}_H \Lambda_v \le \tfrac{\psi_\Gamma(v)}{\min{(v_1, v_2)} }.$$
We also study the local behavior of the higher rank Patterson-Sullivan measures
on each $\Lambda_v$.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol