初始数据集的Willmore质心
The Willmore center of mass of initial data sets
摘要：
我们改进了最近论文arxiv：2101.12665中开发的Lyapunov-Schmidt分析，通过爱因斯坦场方程初始数据的面积约束Willmore表面来研究渐进叶理的几何质量中心。如果初始数据的数量曲率在无穷远处为零，我们证明这个几何质心与哈密顿质心一致。相比之下，我们表明，大面积约束的Willmore表面的位置是敏感的能量密度的分布。特别地，如果数量曲率不满足渐近对称假设，则几何质心可以不同于哈密顿质心。
英文摘要：
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.
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