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On the deformation of discrete conformal factors on surfaces
Luo (Commun Contemp Math 6:765–780, 2004) conjectured that the discrete Yamabe flow will converge to the constant curvature PL-metric after finite number of surgeries on the triangulation. In this…
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Combinatorial Calabi flows on surfaces
For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of smooth Calabi flow. We prove that the solution of combinatorial Calabi flow exists for all time.…
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On the deformation of inversive distance circle packings, III
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Bondi-Sachs metrics and photon rockets
We study the Bondi-Sachs rockets with nonzero cosmological constant. We observe that the acceleration of the systems arises naturally in the asymptotic symmetries of (anti-) de Sitter spacetimes.…
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Kazdan–Warner equation on graph in the negative case
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On the deformation of inversive distance circle packings
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Liouville-type theorems on the complete gradient shrinking Ricci solitons
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A p-th Yamabe equations on graph
Assume $\alpha\geq p>1$. Consider the following $p$-th Yamabe equation on a connected finite graph $G$: $$\Delta_p\varphi+h\varphi^{p-1}=\lambda f\varphi^{\alpha-1},$$ where $\Delta_p$ is the…
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2-dimensional combinatorial Calabi flow in hyperbolic background geometry
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Kazdan-Warner equation on infinite graphs
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…
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