论文标题
局部空间时间常数平均曲率和恒定膨胀叶子
Local space time constant mean curvature and constant expansion foliations
论文作者
论文摘要
受小球体限制的启发，我们研究了具有规定的平均曲率的表面的局部叶子。遵循YE在1991年使用的策略来研究局部恒定平均曲率叶子，我们在n+1维歧管中使用Lyapunov Schmidt减少，配备了对称的2 tensor来构造围绕一个点的叶子，证明其独特性并表现出其不存在的条件。具体来说，我们研究了两个叶面条件。首先，我们考虑恒定的时空平均曲率表面。 Cederbaum和Sakovich使用了这些叶子来表征一般相对论的质量中心。其次，我们研究恒定膨胀表面的局部叶子。
Inspired by the small sphere-limit for quasi-local energy we study local foliations of surfaces with prescribed mean curvature. Following the strategy used by Ye in 1991 to study local constant mean curvature foliations, we use a Lyapunov Schmidt reduction in an n+1 dimensional manifold equipped with a symmetric 2-tensor to construct the foliations around a point, prove their uniqueness and show their nonexistence conditions. To be specific, we study two foliation conditions. First we consider constant space-time mean curvature surfaces. These foliations were used by Cederbaum and Sakovich to characterize the center of mass in general relativity. Second, we study local foliations of constant expansion surfaces.
