Calculus of Variations and Geometric Measure Theory

L. Dufloux

The case of equality in the dichotomy of Mohammadi-Oh

created by dufloux on 10 Feb 2020


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


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 Burger–Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.

Tags: GeoMeG
Keywords: Patterson-Sullivan measure, Kleinian groups, Recurrence