Robin capacity and extremal length (Q1312730)

The paper deals with the Robin capacity. At first in some examples the Robin capacity is computed explicitly. It is shown that if \(\Omega,\widetilde{\Omega} \subset \overline{\mathbb{C}}\), are smoothly bounded finitely connected domains with a common boundary set \(A\), \(\Omega\subset \widetilde{\Omega}\), then \(\delta(A)\leq \widetilde{\delta}(A)\), where \(\delta(A)\) denotes the Robin capacity of \(A\) with respect to \(\Omega\) and \(\widetilde{\delta} (A)\) is the Robin capacity of \(A\) with respect to \(\widetilde{\Omega}\). Further it is shown that if \(A\subset \widetilde{A}\) are closed subsets of \(\partial\Omega\), then \(\delta(A)\leq \delta(\widetilde{A})\).