Singular measures on the limit set of a Kleinian group

Woojin Jeon

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arXiv · 1405.4458

Singular measures on the limit set of a Kleinian group

Woojin Jeon

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Abstract

We consider a finitely generated torsion free Kleinian group $H$ and a random walk on $H$ with respect to a symmetric nondegenerate probability measure $\mu$ with finite support. When $H$ is geometrically infinite without parabolics or when $H$ is Gromov hyperbolic with parabolics, we prove that the Patterson-Sullivan measure is singular with respect to the harmonic measure coming from $\mu$.

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Woojin Jeon. 2014-05-18. Singular measures on the limit set of a Kleinian group. https://arxiv.org/abs/1405.4458

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