Article
Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN
Author/s | Alarcón, Antonio
Fernández Delgado, Isabel López, Francisco J. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2013 |
Deposit Date | 2020-02-20 |
Published in |
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Abstract | We 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 ... We 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. |
Project ID. | MTM2007-61775
MTM2007-64504 P09-FQM-5088 |
Citation | Alarcón, 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. |
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