Density theorems for complete minimal surfaces in R3
Abstract
In this paper we have proved several approximation theorems for the family of minimal surfaces in R3 that imply, among other things, that complete minimal surfaces are dense in the space of all minimal surfaces endowed with the topology of Ck convergence on compact sets, for any k. As a consequence of the above density result, we have been able to produce the first example of a complete proper minimal surface in R3 with uncountably many ends.
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