Kuramochi boundaries of infinite networks and extremal problems (Q1336492)

Discrete potential theory has been developed by several authors, e.g., R. J. Duffin and M. Yamasaki among others, and analogies of various potential theoretic properties of Riemann surfaces have been discussed on infinite networks. We are concerned with the Kuramochi boundaries of infinite networks. We give some examples of Kuramochi functions on infinite networks and the corresponding Kuramochi boundaries. We study extremal problems related to the Kuramochi boundary; the relation between the extremal distance and the Dirichlet principle related to the Kuramochi boundary, and the relation between the extremal width and the flow problem with respect to the Kuramochi boundary.