$\mathbb{R}^3$中有限全曲率完备极小曲面的均匀逼近
微分几何
2015-03-13 v7 代数几何
摘要
得到了极小曲面可由中有限全曲率的完备极小曲面逼近的一个定理。这个Mergelyan类型的结果可以推广到弱有限全曲率的完备极小曲面族，即在有限共形类型的适当区域上具有有限全曲率的曲面。我们仅处理可定向的情形。
引用
@article{arxiv.0903.3209,
title = {Uniform Approximation by Complete Minimal Surfaces of Finite Total Curvature in $\mathbb{R}^3$},
author = {Francisco J. Lopez},
journal= {arXiv preprint arXiv:0903.3209},
year = {2015}
}
备注
24 pages, 3 figures, research article. This updated version introduces considerably simplifications of notations and arguments, and includes some improvements of the results. The paper will appear in the Transactions of the American Mathematical Society