论文标题
高阶$ q $ curvature方程的存在结果
Existence results for the higher-order $Q$-curvature equation
论文作者
论文摘要
我们获得了$ q $ c的订单方程的存在结果$ 2K $在封闭的Riemannian dimensian $ n \ ge 2k+1 $的封闭歧管上，其中$ k \ ge1 $是整数。我们在以下假设下获得了这些结果：订单$ 2K $的Yamabe不变性是正的，并且相应运算符的绿色功能是正，例如，当歧管是Einstein具有正标曲率的爱因斯坦时，这是满足的。如果$ 2K+1 \ le n \ le2k+3 $或$（m，g）$在本地固定时，我们还假设操作员具有正质量。如果$ n \ ge2k+4 $和$（m，g）$不是本地固定的，那么结果基本上减少了仅根据$ n $和$ k $的确定复杂常数的确定。
We obtain existence results for the $Q$-curvature equation of order $2k$ on a closed Riemannian manifold of dimension $n\ge 2k+1$, where $k\ge1$ is an integer. We obtain these results under the assumptions that the Yamabe invariant of order $2k$ is positive and the Green's function of the corresponding operator is positive, which are satisfied for instance when the manifold is Einstein with positive scalar curvature. In the case where $2k+1\le n\le2k+3$ or $(M,g)$ is locally conformally flat, we assume moreover that the operator has positive mass. In the case where $n\ge2k+4$ and $(M,g)$ is not locally conformally flat, the results essentially reduce to the determination of the sign of a complicated constant depending only on $n$ and $k$.
