Kazdan-Warner equation on infinite graphs
Analysis of PDEs
2017-06-28 v1
Abstract
We concern in this paper the graph Kazdan-Warner equation \begin{equation*} \Delta f=g-he^f \end{equation*} on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that and some other integrability conditions or constrictions about the underlying infinite graphs.
Cite
@article{arxiv.1706.08698,
title = {Kazdan-Warner equation on infinite graphs},
author = {Huabin Ge and Wenfeng Jiang},
journal= {arXiv preprint arXiv:1706.08698},
year = {2017}
}