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

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

2009-03-18

arxiv.org/abs/0903.3209v6

Mathematics

Differential Geometry

24 pages, 3 figures, research article. This updated version introduces considerably simplifications of notations and arguments

Scientific paper

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.

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