论文标题
（分支）覆盖地图的表面之间的谐波图
Harmonic maps between surfaces homotopic to a (branched) covering map
论文作者
论文摘要
在论文中，我们考虑了（分支）覆盖地图$ u_0 $的同型类别的表面$σ$和$ s $之间的谐波图。如果$ u_0 $是覆盖地图，我们证明了能量功能关键点的唯一性和Hopf差分的注入性。另一方面，如果$ u_0 $是分支的覆盖物，我们表明，如果$ u_0 $是一个非简单的分支覆盖物，关键点的独特性会失败，并证明了hopf差异$φ的注入性：\ mc {t}（t}（t}（s）） $ S $。
In the paper, we consider the harmonic maps between surfaces $Σ$ and $S$ in the homotopy class of a (branched) covering map $u_0$. We prove the uniqueness of critical points of energy function and the injectivity of Hopf differential if $u_0$ is a covering map. On the other hand, if $u_0$ is a branched covering, we show that the uniqueness of critical points fails if $u_0$ is a non-simple branched covering, and prove the injectivity of Hopf differential $Φ:\mc{T}(S)\to \op{QD}(Σ,g)$ when $g=[u_0^* h]$ for some hyperbolic metric $h$ on $S$.
