论文标题
Riemann表面Orbifolds上均匀的奇异射击结构
Uniformizable singular projective structures on Riemann surface orbifolds
论文作者
论文摘要
本文致力于表征在Riemann表面Orbifolds上定义的复杂投影结构，并引起了所讨论的表面（Orbifold）单层覆盖的注入性开发图。这些结构的相关性源于涉及具有均匀溶液的向量场以及关于Riemann表面叶子叶子的“同时均匀化”的问题。在本文中，我们首先描述了提到的投影结构的局部结构，特别是显示它们是局部界限的。在有限类型的Riemann表面Orbifolds的情况下，先前的结果将使我们能够通过利用其与“有限覆盖的投影结构”类别的连接来提供这些投射结构的详细全局图片。
This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance of these structures stems from several problems involving vector fields with uniform solutions as well as from problems about "simultaneous uniformization" for leaves of foliations by Riemann surfaces. In this paper, we first describe the local structure of the mentioned projective structures showing, in particular, that they are locally bounded. In the case of Riemann surface orbifolds of finite type, the previous result will then allow us to provide a detailed global picture of these projective structures by exploiting their connection with the class of "bounded covering projective structures".
