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KAZDAN-WARNER EQUATION ON INFINITE GRAPHS
Ge, Huabin,Jiang, Wenfeng Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5
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.
Kazdan-Warner equation on infinite graphs
Huabin Ge,Wenfeng Jiang 대한수학회 2018 대한수학회지 Vol.55 No.5
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.
Unified (α, β)-flows on triangulated manifolds with two and three dimensions
Huabin Ge,Ming Li 대한수학회 2017 대한수학회보 Vol.54 No.4
In this paper, we introduce a framework of $(\alpha,\beta)$-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.
UNIFIED (α, β)-FLOWS ON TRIANGULATED MANIFOLDS WITH TWO AND THREE DIMENSIONS
Ge, Huabin,Li, Ming Korean Mathematical Society 2017 대한수학회보 Vol.54 No.4
In this paper, we introduce a framework of (${\alpha},{\beta}$)-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.