The Kazdan-Warner equation on canonically compactifiable graphs (Q1751610)

In last years several topics in the analysis on graphs received a lot of attention. The Kazdan-Warner equation arises from the basic geometric question which functions are potential Gaussian curvature for 2d manifolds. The present paper studies this equation on so-called \textit{canonically compactifiable} graphs under the assumption that the graph has finite measure. One useful characterization of this class of graphs is that functions of finite energy are already bounded. A main tool in this study is the Neumann-Laplacian which is the self-adjoint operator associated to a quadratic form on all \(l^2\)-functions of finite energy. Solutions are then required to be in the operator domain of the Neumann-Laplacian.