标题： 静态完美流体时空的几何学 显示英文标题

标题： Geometry of static perfect fluid space-time

摘要： 本文研究了紧致带边流形上的静态完美流体时空的几何性质。我们利用广义Reilly公式建立了一个涉及边界面积和体积的静态完美流体时空的几何不等式。此外，我们还得到了静态完美流体时空的新边界估计。其中一个边界估计以Brown-York质量表示，另一个与Jacobi算子的第一特征值有关。另外，我们为任意维数提供了宇宙无毛猜想的一个新的（单连通）反例，记为$n\geq 4.$。 显示英文摘要

摘要： In this article, we investigate the geometry of static perfect fluid space-time on compact manifolds with boundary. We use the generalized Reilly's formula to establish a geometric inequality for a static perfect fluid space-time involving the area of the boundary and its volume. Moreover, we obtain new boundary estimates for static perfect fluid space-time. One of the boundary estimates is obtained in terms of the Brown-York mass and another one related to the first eigenvalue of the Jacobi operator. In addition, we provide a new (simply connected) counterexample to the Cosmic no-hair conjecture for arbitrary dimension $n\geq 4.$