Intrinsic geometry and boundary structure of plane domains

Oona Rainio, Toshiyuki Sugawa, Matti Vuorinen

For a non-empty compact set $E$ in a proper subdomain $\Omega$ of the complex plane, we denote the diameter of $E$ and the distance from $E$ to the boundary of $\Omega$ by $d(E)$ and $d(E,\p…