论文标题
双曲线四个空间中给定的共形类型的适当的超微小表面
Proper superminimal surfaces of given conformal types in the hyperbolic four-space
论文作者
论文摘要
令$ h^4 $表示双曲线四个空间。鉴于边界的riemann表面，$ m $，我们证明，每种光滑的共形超金融浸入$ \叠加级别的m \ to h^4 $都可以通过适当的保形超超级浸入$ m $均匀地近似于$ m $的紧凑型，以h^4 $。尤其是，$ h^4 $包含适当浸入的共形超微小表面，该表面由任何给定的有限拓扑类型的开放式黎曼表面归一化，没有穿刺。该证明使用$ H^4 $的扭曲器空间中的Holomorphic Legendrian曲线分析。
Let $H^4$ denote the hyperbolic four-space. Given a bordered Riemann surface, $M$, we prove that every smooth conformal superminimal immersion $\overline M\to H^4$ can be approximated uniformly on compacts in $M$ by proper conformal superminimal immersions $M\to H^4$. In particular, $H^4$ contains properly immersed conformal superminimal surfaces normalised by any given open Riemann surface of finite topological type without punctures. The proof uses the analysis of holomorphic Legendrian curves in the twistor space of $H^4$.
