Kazdan-Warner equation on infinite graphs

2017/06/27 by Huabin Ge, Ge, Huabin, Wenfeng Jiang +1 · 8 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1706.08698

Abstract

We concern in this paper the graph Kazdan-Warner equation Δf=g-he^f 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≤0 and some other integrability conditions or constrictions about the underlying infinite graphs.

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