论文标题
$σ_{2} $ penrose不平等渐近屈曲4盘
A $σ_{2}$ Penrose inequality for conformal asymptotically hyperbolic 4-discs
论文作者
论文摘要
在本文中，我们考虑在具有渐近双曲线端和可能的孤立圆锥奇点的4盘单位上的共形度量。我们定义了AH终点的质量。如果$σ_{2} $曲率具有下限$σ_{2} \ geq \ frac {3} {2} $，我们证明了penrose类型的不平等，将质量和来自奇点的贡献涉及。我们还对尖锐的情况进行了分类，这是标准双曲线4空间$ \ mathbb {h}^{4} $当不发生奇点时。值得注意的是，我们的曲率条件意味着非阳性能量密度。
In this paper, we consider conformal metrics on a unit 4-disc with an asymptotically hyperbolic end and possible isolated conic singularities. We define a mass term of the AH end. If the $σ_{2}$ curvature has lower bound $σ_{2}\geq\frac{3}{2}$, we prove a Penrose type inequality relating the mass and contributions from singularities. We also classify sharp cases, which is the standard hyperbolic 4-space $\mathbb{H}^{4}$ when no singularity occurs. It is worth noting that our curvature condition implies non-positive energy density.
