Potential theory on infinite networks
The book gives an unified approach to new developments in the theory of infinite networks. Starting by describing and exploring the model of a network and by studying the elementary properties of currents, resistances etc. the note then gives the basic results of infinite networks, existence theorems and Yamasaki's potential theory (restricting the investigation to currents and problems of finite energy). A further chapter is devoted to the problem of uniqueness. After applying the theory to study some particular networks, the Royden compactification of a network along the lines of Royden's compactification for Riemannian manifolds is defined and studied. A final chapter is devoted to rough isometries.
scientific article; zbMATH DE number 692290