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Let Z be a so-called well-behaved percolation, i.e. a certain random closedset in the hyperbolic plane, whose law is invariant under all isometries; forexample the covered region in a Poisson Boolean model. The Hausdorff-dimensionof the set of directions is determined in terms of the $\alpha$-value of Z inwhich visibility from a fixed point to the ideal boundary of the hyperbolicplane is possible within Z. Moreover, the Hausdorff-dimension of the set of(hyperbolic) lines through a fixed point contained in Z is calculated. Therebyseveral conjectures raised by Benjamini, Jonasson, Schramm and Tykesson areconfirmed.

Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane