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

Authors: Antonio Alarcón and Francisco J. López
Journal: Trans. Amer. Math. Soc. 365 (2013), 1711-1742
MSC (2010): Primary 53C43, 53C42, 30F15
Published electronically: September 26, 2012
MathSciNet review: 3009644
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Abstract: 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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Additional Information

Antonio Alarcón
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain

Francisco J. López
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain

Keywords: Harmonic immersions of Riemann surfaces, quasiconformal mappings, Gauss map
Received by editor(s): February 21, 2011
Published electronically: September 26, 2012
Additional Notes: This research was partially supported by MCYT-FEDER research projects MTM2007-61775 and MTM2011-22547, and Junta de Andalucía Grant P09-FQM-5088
The first author was also supported by Vicerrectorado de Política Científica e Investigación de la Universidad de Granada, and by the grant PYR-2012-3 CEI BioTIC GENIL (CEB-09-0010) of the MICINN CEI Program
Article copyright: © Copyright 2012 American Mathematical Society

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