Year: 2017
Type: preprint
Abstract: We concern in this paper the graph Kazdan-Warner equation \begin{equation*} Δf=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 $h\leq0$ and some other integrability conditions or constrictions about the underlying infinite graphs.
Source: arXiv (Cornell University)
Authors: Ge, Huabin, Jiang, Wenfeng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1525990181, G374582687
OpenAlex ID: W2734069799