标题： 简单数值解在各种三维流形上的爱因斯坦约束条件 显示英文标题

标题： Simple Numerical Solutions to the Einstein Constraints on Various Three-Manifolds

摘要： 对具有非平凡拓扑的紧致可定向三维流形上爱因斯坦约束方程的数值解被构造出来。 在八种 Thursten 几何化类中的三种示例流形上计算了一个简单的常平均曲率解和一个稍显复杂的非常平均曲率解。 此处找到的常平均曲率解也是将几何转换为具有常标量曲率的 Yamabe 问题的解。 显示英文摘要

摘要： Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated non-constant mean curvature solution are computed on example manifolds from three of the eight Thursten geometrization classes. The constant mean curvature solutions found here are also solutions to the Yamabe problem that transforms a geometry into one with constant scalar curvature.