论文标题
$ \ mathbb {r}^4 $ demaneratingpoincaré-enstein指标的家庭家庭
Families of degenerating Poincaré-Einstein metrics on $\mathbb{R}^4$
论文作者
论文摘要
我们提供了庞加莱 - 因斯坦（Poincaré-Einstein）指标连续家庭的第一个例子，开发了关于微不足道的拓扑$ \ mathbb {r}^4 $。我们还展示了仅在共形无穷大的情况下出现意外退化的指标家族。这些是从Debever和Plebański-Demiański的Riemannian版本中获得的。我们还指出了如何在更复杂的拓扑结构上构建类似的例子。
We provide the first example of continuous families of Poincaré-Einstein metrics developing cusps on the trivial topology $\mathbb{R}^4$. We also exhibit families of metrics with unexpected degenerations in their conformal infinity only. These are obtained from the Riemannian version of an ansatz of Debever and Plebański-Demiański. We additionally indicate how to construct similar examples on more complicated topologies.
