Artículo
Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN
Autor/es | Alarcón, Antonio
Fernández Delgado, Isabel ![]() ![]() ![]() ![]() ![]() ![]() ![]() López, Francisco J. |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2013 |
Fecha de depósito | 2020-02-20 |
Publicado en |
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Resumen | 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. |
Identificador del proyecto | MTM2007-61775
![]() MTM2007-64504 ![]() P09-FQM-5088 ![]() |
Cita | 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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