论文标题
初始数据集的质量中心
The Willmore center of mass of initial data sets
论文作者
论文摘要
我们完善了在最近的论文ARXIV：2101.12665中开发的Lyapunov-Schmidt分析，以研究爱因斯坦田间方程的初始数据的面积构成的Willmore表面，研究了渐近叶片的质量几何中心。如果初始数据的标态曲率在无穷大处消失，我们表明这个质量的几何中心与汉密尔顿质量中心一致。相比之下，我们表明，大面积约束的Willmore表面的位置对能量密度的分布敏感。特别是，如果标量曲率不满足渐近的对称性假设，则质量的几何中心可能与哈密顿质量中心不同。
We refine the Lyapunov-Schmidt analysis developed in our recent paper arxiv:2101.12665 to study the geometric center of mass of the asymptotic foliation by area-constrained Willmore surfaces of initial data for the Einstein field equations. If the scalar curvature of the initial data vanishes at infinity, we show that this geometric center of mass agrees with the Hamiltonian center of mass. By contrast, we show that the position of large area-constrained Willmore surfaces is sensitive to the distribution of the energy density. In particular, the geometric center of mass may differ from the Hamiltonian center of mass if the scalar curvature does not satisfy asymptotic symmetry assumptions.
