关于Schwarzschild-de Sitter时空的唯一性
On the uniqueness of Schwarzschild-de Sitter spacetime
摘要：
我们建立了三维Schwarzschild-de Sitter度量的一个新的唯一性定理。为此，开发了一些新的或改进的工具。其中包括一个反向Lojasiewicz不等式，它在任何光滑函数的极值点附近成立。我们进一步证明了光滑的一组最大值的流逝，每当这一组包含一个拓扑超曲面。这导致了一个新的战略分类的良好表现的静态解决方案的爱因斯坦方程具有积极的宇宙学常数，根据几何形状的最大集的流逝。
英文摘要：
We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this some new or improved tools are developed. These include a reverse Lojasiewicz inequality, which holds in a neighborhood of the extremal points of any smooth function. We further prove smoothness of the set of maxima of the lapse, whenever this set contains a topological hypersurface. This leads to a new strategy for the classification of well behaved static solutions of Einstein equations with a positive cosmological constant, based on the geometry of the maximum-set of the lapse.
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