Density theorems for complete minimal surfaces in R^3
微分几何
2007-05-23 v3
摘要
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.
引用
@article{arxiv.math/0603737,
title = {Density theorems for complete minimal surfaces in R^3},
author = {A. Alarcon and L. Ferrer and F. Martin},
journal= {arXiv preprint arXiv:math/0603737},
year = {2007}
}
备注
32 pages, 8 figures. To appear in G.A.F.A