2020-02-202020-02-202013Alarcón, A., Fernández Delgado, I. y López, F.J. (2013). Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN. Calculus of Variations and Partial Differential Equations, 47 (1-2), 227-242.0944-2669https://hdl.handle.net/11441/93474We prove that for any open Riemann surface N, natural number N ≥ 3, non-constant harmonic map h:N→R N−2 and holomorphic 2-form H on N , there exists a weakly complete harmonic map X=(Xj)j=1,…,\scN:N→R\scN with Hopf differential H and (Xj)j=3,…,\scN=h. In particular, there exists a complete conformal minimal immersion Y=(Yj)j=1,…,\scN:N→R\scN such that (Yj)j=3,…,\scN=h . As some consequences of these results (1) there exist complete full non-decomposable minimal surfaces with arbitrary conformal structure and whose generalized Gauss map is non-degenerate and fails to intersect N hyperplanes of CP\scN−1 in general position. (2) There exist complete non-proper embedded minimal surfaces in R\scN, ∀\scN>3.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Complete minimal surfacesHarmonic mapping of Riemann surfacesGauss mapinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/s00526-012-0517-020311642