Density theorems for complete minimal surfaces in R^3
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In this paper we have proved several approximation theorems for the family of minimal surfaces in R^3 that imply, among other things, that complete minimal surfaces are dense in the space of all minimal surfaces endowed with the topology of C^k 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 R^3 with uncountably many ends.
32 pages, 8 figures. To appear in G.A.F.A
32 pages, 8 figures. To appear in G.A.F.A