Kazdan-Warner equation on infinite graphs

By Huabin Ge, Wenfeng Jiang. 2017

62 citations recorded by the source corpus.

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 $h\leq0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5e464dec50f6cfe2314da7c223db49d4418f135c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Matthias Keller
2. Michael Schwarz

In Computational Theory and Mathematics

1. Michael Schwarz
2. Matthias Keller

Citations in the corpus

• The Kazdan–Warner equation on canonically compactifiable graphs (2017, background): “Note added After this work was completed we learned about the recent preprint of Ge and Jiang [15].”