发表机构
Southern University of Science and Technology; SUSTech International Center for Mathematics; Hebei Normal University（南方科技大学; 南方科技大学国际数学中心; 河北师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明满足条件A的有限拓扑型完备曲面同胚于二维环面，且孤立平面端非周期，部分回答了此类曲面是否紧致的问题。
AI 中文摘要
我们证明，满足条件A的有限拓扑型完备曲面同胚于二维环面。更一般地，我们表明，满足条件A的完备开曲面的孤立平面端在端空间上的诱导作用下不能是周期的。条件A包括稠密周期点、对于完备度量的一维子丛的一致双曲分裂，以及唯一积分成横截稳定与不稳定叶状结构的不变线场。这些结果对满足条件A的完备曲面是否必定紧致的问题给出了部分回答。
英文摘要
We prove that a complete surface of finite topological type satisfying Condition A is homeomorphic to the two-torus. More generally, we show that an isolated planar end of a complete open surface satisfying Condition A cannot be periodic under the induced action on the space of ends. Condition A includes dense periodic points, a uniformly hyperbolic splitting into one-dimensional subbundles for a complete metric, and invariant line fields that uniquely integrate to transverse stable and unstable foliations. These results give a partial answer to the question of whether a complete surface satisfying Condition A must be compact.
