论文标题
Riemannian模型上的径向解决方案分类为$-Δ_Gu = e^u $
Classification of radial solutions to $-Δ_g u=e^u$ on Riemannian models
论文作者
论文摘要
我们提供了关于径向平滑解决方案对等式$-Δ_Gu = e^u $的渐近行为，稳定性和相交属性的完整分类，而Riemannian模型歧管上的$（m，g）$ in Dimension $ n \ ge 2 $。我们的假设包括从下方有界面或无限制的截面曲率的Riemannian歧管。径向解决方案的交集和稳定性属性受尺寸$ n $的影响，即当分别为$ 2 \ leq n \ le 9 $或$ n \ geq 10 $时发生两种不同的行为。这些维度在分类溶液中的关键作用在欧几里得空间中众所周知。
We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation $-Δ_g u=e^u$ on Riemannian model manifolds $(M,g)$ in dimension $N\ge 2$. Our assumptions include Riemannian manifolds with sectional curvatures bounded or unbounded from below. Intersection and stability properties of radial solutions are influenced by the dimension $N$ in the sense that two different kinds of behaviour occur when $2\leq N\le 9$ or $N\geq 10$, respectively. The crucial role of these dimensions in classifying solutions is well-known in Euclidean space.
