On harmonic quasiconformal immersions of surfaces in $\mathbb{R}^3$

Mathematics – Differential Geometry

Scientific paper

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

Scientific paper

This paper is devoted to the study of the global properties of harmonically
immersed Riemann surfaces in $\mathbb{R}^3.$ 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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