论文标题
Riemann表面的封闭连续
Closed continuations of Riemann surfaces
论文作者
论文摘要
任何开放的Riemann Surface $ r_0 $ r_0 $ r_0 $ g $都可以固定地嵌入同一属的封闭riemann表面中，即，$ r_0 $被实现为$ g $属的封闭riemann表面的子域。我们关注此类封闭的Riemann表面的集合$ M（R_0）$。我们在TeichMüller空间设置中提出问题，以研究$ M（R_ {0}）$的几何属性。除其他外，我们表明$ m（r_ {0}）$是封闭的lipschitz域同构，只要$ r_0 $是无分析的有限的。
Any open Riemann surface $R_0$ of finite genus $g$ can be conformally embedded into a closed Riemann surface of the same genus, that is, $R_0$ is realized as a subdomain of a closed Riemann surface of genus $g$. We are concerned with the set $M(R_0)$ of such closed Riemann surfaces. We formulate the problem in the Teichmüller space setting to investigate geometric properties of $M(R_{0})$. We show, among other things, that $M(R_{0})$ is a closed Lipschitz domain homeomorphic to a closed ball provided that $R_0$ is nonanalytically finite.
