*Published Paper*

**Inserted:** 10 feb 2020

**Journal:** Journal of Fractal Geometry

**Volume:** 6

**Number:** 4

**Pages:** 343-366

**Year:** 2019

**Doi:** 10.4171/JFG

**Links:**
Link to the paper

**Abstract:**

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o (1,n+1)$ such that $\delta_\Gamma = n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burgerâ€“Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.

**Tags:**
GeoMeG

**Keywords:**
Patterson-Sullivan measure, Kleinian groups, Recurrence