论文标题
谐波分支覆盖物和猫（$ k $）球的均匀化
Harmonic branched coverings and uniformization of CAT($k$) spheres
论文作者
论文摘要
令$ s $为一个公制$ d $的表面，满足亚历山大洛夫（Alexandrov）意义上的上曲率（即通过三角比较）。我们表明，从表面到$（s，d）$的几乎保形谐波图是一个分支覆盖。结果，如果$（s，d）$同词同等等同于2-sphere $ \ mathbb s^2 $，则它在$ \ Mathbb s^2 $上相当于。
Let $S$ be a surface with a metric $d$ satisfying an upper curvature bound in the sense of Alexandrov (i.e. via triangle comparison). We show that an almost conformal harmonic map from a surface into $(S,d)$ is a branched covering. As a consequence, if $(S,d)$ is homeomorphically equivalent to the 2-sphere $\mathbb S^2$, then it is conformally equivalent to $\mathbb S^2$.
