论文标题
渐近双曲线端和距离估计值的质量
The mass of an asymptotically hyperbolic end and distance estimates
论文作者
论文摘要
Let $(M,g)$ be a complete connected $n$-dimensional Riemannian spin manifold without boundary such that the scalar curvature satisfies $R_g\geq -n(n-1)$ and $\mathcal{E}\subset M$ be an asymptotically hyperbolic end, we prove that the mass functional of the end $\mathcal{E}$ is timelike future-directed or 零。此外，当且仅当$（m，g）$与双曲线空间等值时，它会消失。我们还考虑了一个渐近边界的渐近双曲线歧管的质量，如果边界的平均曲率通过使用距离估计的函数定义的函数，则证明质量是定时指导的。作为一种应用，如果边界的平均曲率从下方限制为$ - （n-1）$或标量曲率满足$ r_g \ geq（-1+κ）n（n-1）$，那么任何正常常数$κ$小于一个。
Let $(M,g)$ be a complete connected $n$-dimensional Riemannian spin manifold without boundary such that the scalar curvature satisfies $R_g\geq -n(n-1)$ and $\mathcal{E}\subset M$ be an asymptotically hyperbolic end, we prove that the mass functional of the end $\mathcal{E}$ is timelike future-directed or zero. Moreover, it vanishes if and only if $(M,g)$ is isometric to the hyperbolic space. We also consider the mass of an asymptotically hyperbolic manifold with compact boundary, we prove the mass is timelike future-directed if the mean curvature of the boundary is bounded from below by a function defined using distance estimates. As an application, the mass is timelike future-directed if the mean curvature of the boundary is bounded from below by $-(n-1)$ or the scalar curvature satisfies $R_g\geq (-1+κ)n(n-1)$ for any positive constant $κ$ less than one.
