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… Expand

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.… Expand

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.… Expand

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… Expand

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… Expand