论文标题
分数Yamabe问题的奇异解决方案的定性特性
Qualitative Properties of Singular Solutions to the Fractional Yamabe Problem
论文作者
论文摘要
在本文中，我们对$ \ mathbb {r}^n $中分数Yamabe问题的解决方案的定性属性感兴趣，这些属性具有孤立的奇异性。特别是，我们证明了任何此类解决方案的摩尔斯指数是无穷大的。证明使用Emden Fowler类型转换，因此我们可以传递到$ \ Mathbb {r} $中的非本地1D问题。
In this paper we are interested in the qualitative properties of the solutions to the fractional Yamabe problem in $\mathbb{R}^n$ which present an isolated singularity. In particular, we prove that the Morse index of any such solution is infinity. The proof uses a Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in $\mathbb{R}$.
