2018/06/08 by Meeks, William H., Perez, Joaquin, Ros, Antonio · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1806.03104
Suppose M is a complete, embedded minimal surface in ℝ3 with an infinite number of ends, finite genus and compact boundary. We prove that the simple limit ends of M have properly embedded representatives with compact boundary, genus zero and with constrained geometry. We use this result to show that if M has at least two simple limit ends, then M has exactly two simple limit ends. Furthermore, we demonstrate that M is properly embedded in ℝ3 if and only if M has at most two limit ends if and only if M has a countable number of limit ends.