Geodesic
A property of purely hyperbolic Fuchsian groups of the second kind
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 177-183 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a purely hyperbolic finitely generated non-elementary Fuchsian group of the second kind. If $\Lambda$ is the limit set of the group $G$, then the function $\log(\mathrm{dist}\,(x,\Lambda))$ belongs to the class BMO. This follows from the fact that $\Lambda$ is porous, which is proved in the paper. 
@article{ZNSL_1998_255_a11,
     author = {O. L. Semenova},
     title = {A property of purely hyperbolic {Fuchsian} groups of the second kind},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--183},
     year = {1998},
     volume = {255},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a11/}
}
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O. L. Semenova. A property of purely hyperbolic Fuchsian groups of the second kind. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 177-183. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a11/