论文标题
RICCI曲率的边界和对加权图的爱因斯坦方程的解决方案
Bounds on the Ricci curvature and solutions to the Einstein equations for weighted graphs
论文作者
论文摘要
这是基于图上的lin-lu-yau ricci曲率，对图表上欧几里得经典重力运动方程的初步研究。我们观察到，恒定边缘配置为无限树W.R.T.上提供了独特的解决方案。渐近恒定边界条件。我们研究动作W.R.T.的最小和最大值某些边界条件，在几种类型的关注图上。我们还向无限常规树上的运动方程式展示了一类新的解决方案。
This is a preliminary study of the equation of motion of Euclidean classical gravity on a graph, based on the Lin-Lu-Yau Ricci curvature on graphs. We observe that the constant edge weights configuration gives the unique solution on an infinite tree w.r.t. the asymptotically constant boundary condition. We study the minimum and maximum of the action w.r.t. certain boundary conditions, on several types of graphs of interest. We also exhibit a new class of solutions to the equations of motion on the infinite regular tree.
