We apply the local removable singularity theorem for minimal laminations [W. H. Meeks III, J. Pérez and A. Ros, Local removable singularity theorems for minimal laminations, J. Differential Geom. 103 (2016), no. 2, 319–362] and the local picture theorem on the scale of topology [W. H. Meeks III, J. Pérez and A. Ros, The local picture theorem on the scale of topology, J. Differential Geom. 109 (2018), no. 3, 509–565] to obtain two descriptive results for certain possibly singular minimal laminations of ${ℝ}^3$. These two global structure theorems will be applied in [W. H. Meeks III, J. Pérez and A. Ros, Bounds on the topology and index of classical minimal surfaces, preprint 2016] to obtain bounds on the index and the number of ends of complete, embedded minimal surfaces of fixed genus and finite topology in ${ℝ}^3$, and in [W. H. Meeks III, J. Pérez and A. Ros, The embedded Calabi–Yau conjectures for finite genus, preprint 2018] to prove that a complete, embedded minimal surface in ${ℝ}^3$ with finite genus and a countable number of ends is proper.

中文翻译：

---

奇异极小叠片的结构定理

我们将局部可移动奇点定理应用于最小化叠层[W. H. Meeks III，J。Pérez和A. Ros，最小化叠层的局部可移动奇点定理，J。Differential Geom。103（2016），第 [2，319–362]和局部图片定理在拓扑学上的规模[W. H. Meeks III，J。Pérez和A. Ros，关于拓扑规模的局部图像定理，J。Differential Geom。109（2018），第 3，509-565]，以获得某些可能的两个描述性结果的奇异最小叠片的${ℝ}^3$。这两个全局结构定理将在[W. H. Meeks III，J。Pérez和A. Ros，经典最小曲面的拓扑和索引上的界限，预印本[2016]，以获得索引的界限以及固定类和有限拓扑的完整，嵌入式最小曲面的末端数在${ℝ}^3$，并在[W. H. Meeks III，J。Pérez和A. Ros，有限类的嵌入式Calabi–Yau猜想，预印本，2018年），以证明在${ℝ}^3$ 具有有限的属并且末端数目可观是适当的。