论文标题
爱因斯坦对各种三序列的约束的简单数值解决方案
Simple Numerical Solutions to the Einstein Constraints on Various Three-Manifolds
论文作者
论文摘要
爱因斯坦约束方程的数值解决方案是在具有非平凡拓扑结构的可定向的三维流形的选择上构建的。根据八个瑟斯滕几何化类别中的三个中的三个，计算了一个简单的常数平均曲率解和更复杂的非恒定平均曲率解。这里发现的恒定平均曲率溶液也是Yamabe问题的解决方案，该解决方案将几何形状转化为具有恒定标态曲率的几何形状。
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.
