论文标题
关于平面恒定正曲率的共形指标
On conformal metrics of constant positive curvature in the plane
论文作者
论文摘要
我们证明了有关$ΔU + e^{2u} = 0 $的解决方案的三个定理。前两个明确描述了所有凹形和Quasiconcave解决方案。第三个定理说，平面的直径相对于用线元素$ e^{u} | dz | $的指标，至少为$4π/3 $，除了两个明确描述的解决方案家族u。
We prove three theorems about solutions of $Δu + e^{2u} = 0$ in the plane. The first two describe explicitly all concave and quasiconcave solutions. The third theorem says that the diameter of the plane with respect to the metric with line element $e^{u}|dz|$ is at least $4π/3$, except for two explicitly described families of solutions u.
