Uniform Approximation by Complete Minimal Surfaces of Finite Total Curvature in ℝ³

2009/03/18 by Francisco J. Lopez, Lopez, Francisco J.
Mathematics · #49Q05 #49Q10 #53A10 #53C42 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:49Q05 #msc:49Q10 #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.0903.3209

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

arxiv created 2012/06/04 · arxiv updated 2015/03/13

Abstract

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in ℝ³ 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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