论文标题
完整的K曲面歧管的紧凑定理具有孤立的奇异性
Compactness Theorem of Complete k-Curvature Manifolds with Isolated Singularities
论文作者
论文摘要
在本文中，我们证明了$ \ Mathbb {s}^{n} \ backslash \ {p_ {1}，\ cdots，p_ {l} \} $在$ c^{m，α} $ topolation in n y $ c^{m，p_} $ pologial for n $ c^{m，p_} $ topolotic for n $ c^{m，p_} $ topologe， $σ_{k} $曲率和$ k $ -dilational pohozaev不变式的下限为$ k <n/2 $。在这里，$ k $ - diLalational pohozaev不变式来自$σ_{k} $曲率的kazdan-warner类型标识，该标识由Viaclovsky \ cite \ cite {viac2000}和han \ cite {h1}得出。当$ k = 1 $时，Pollack \ Cite {Pollack}证明了$ \ Mathbb {s}^{n} \ backslash \ backslash \ {p_ {1}，\ cdots，p_ {l} \ \} \} $的完整指标的紧凑度结果。
In this paper we prove that the set of metrics conformal to the standard metric on $\mathbb{S}^{n}\backslash\{p_{1},\cdots,p_{l}\}$ is locally compact in $C^{m,α}$ topology for any $m>0$, whenever the metrics have constant $σ_{k}$ curvature and the $k$-Dilational Pohozaev invariants have positive lower bound for $k<n/2$. Here the $k$-Dilational Pohozaev invariants come from the Kazdan-Warner type identity for the $σ_{k}$ curvature, which is derived by Viaclovsky \cite{Viac2000} and Han \cite{H1}. When $k=1$, Pollack \cite{Pollack} proved the compactness results for the complete metrics of constant positive scalar curvature on $\mathbb{S}^{n}\backslash\{p_{1},\cdots,p_{l}\}$.
