Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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KAZDAN-WARNER EQUATION ON INFINITE GRAPHS

  • Ge, Huabin (Department of Mathematics Beijing Jiaotong University) ;
  • Jiang, Wenfeng (School of Mathematics (Zhuhai) Sun Yat-Sen University)
  • Received : 2017.08.26
  • Accepted : 2018.06.07
  • Published : 2018.09.01
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Abstract

We concern in this paper the graph Kazdan-Warner equation $${\Delta}f=g-he^f$$ 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 $h{\leq}0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

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References

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