Accessible Parts of Boundary for Simply Connected Domains

Pekka Koskela, Debanjan Nandi, Artur Nicolau

For a bounded simply connected domain $\Omega \subset {\mathbb{R}}^2$, any point $z\in \Omega$ and any $0<\alpha <1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of point…