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

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.

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

References in corpus (4)

• Density theorems for complete minimal surfaces in R^3
• The Spinor Representation of Minimal Surfaces
• On the existence of a proper minimal surface in $R^3$ with the conformal type of a disk
• Exotic Minimal Surfaces

Cited by in corpus (2)

• Complete minimal surfaces and harmonic functions
• Properness of associated minimal surfaces