AbstractWe 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 {\mathbb{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 {\mathbb{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 {\mathbb{R}^{3}} with finite genus and a countable number
of ends is proper.
Geometric convergence results for closed minimal surfaces via bubbling analysis
