2016/02/17 by Peter Connor, Connor, Peter
Mathematics · #49Q05 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:49Q05 #msc:53A10 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1602.05265
arxiv created 2016/04/28 · arxiv updated 2016/04/29
The Weierstrass representation for minimal surfaces in ℝ3 provides a flexible method for constructing minimal surfaces of arbitrary genus. The topological limitations of minimal surfaces interfere with this providing a more general geometric modeling tool. Minimal surfaces lie in the larger class of harmonic surfaces, which in general don't have the same topological limitations of minimal surfaces and can have complicated embedded ends. In this paper we demonstrate the flexibility of using the Weierstrass representation for harmonic surfaces to combine embedded harmonic ends together to construct embedded harmonic surfaces of arbitrary genus.