On harmonic quasiconformal immersions of surfaces in ℝ³

2011/02/21 by Antonio Alarcon, Alarcon, Antonio, Francisco J. Lopez +1
Mathematics · #30F15 #53C42 #53C43 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:30F15 #msc:53C42 #msc:53C43

paper · pdf · doi:10.48550/arxiv.1102.4260

27 pages, 7 figures. Minor changues. To appear in Trans. Amer. Math. Soc

arxiv created 2011/07/01 · arxiv updated 2011/07/04

Abstract

This paper is devoted to the study of the global properties of harmonically immersed Riemann surfaces in ℝ³. We focus on the geometry of complete harmonic immersions with quasiconformal Gauss map, and in particular, of those with finite total curvature. We pay special attention to the construction of new examples with significant geometry.

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