Uniform Approximation by Complete Minimal Surfaces of Finite Total Curvature in $\mathbb{R}^3$

Francisco J. Lopez

Uniform Approximation by Complete Minimal Surfaces of Finite Total Curvature in $\mathbb{R}^3$

Differential Geometry 2015-03-13 v7 Algebraic Geometry

Authors: Francisco J. Lopez

Abstract

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in $\mathbb{R}^3$ is obtained. This Mergelyan type result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of finite conformal type. We deal only with the orientable case.

Keywords

minimal surfaces complete minimal surfaces finite total curvature uniform approximation Mergelyan theorem orientable surfaces

Cite

@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}
}

Comments

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

Uniform Approximation by Complete Minimal Surfaces of Finite Total Curvature in $\mathbb{R}^3$

Abstract

Keywords

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