Artículo
Harmonic maps and constant mean curvature surfaces in H 2 x R
Autor/es | Fernández Delgado, Isabel
Mira, Pablo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2007 |
Fecha de depósito | 2021-07-06 |
Publicado en |
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Resumen | We introduce a hyperbolic Gauss map into the Poincar´e disk for any surface in H2×R with
regular vertical projection, and prove that if the surface has constant mean curvature H = 1/2, this
hyperbolic Gauss map is harmonic. ... We introduce a hyperbolic Gauss map into the Poincar´e disk for any surface in H2×R with regular vertical projection, and prove that if the surface has constant mean curvature H = 1/2, this hyperbolic Gauss map is harmonic. Conversely, we show that every nowhere conformal harmonic map from an open simply connected Riemann surface Σ into the Poincar´e disk is the hyperbolic Gauss map of a two-parameter family of such surfaces. As an application we obtain that any holomorphic quadratic differential on Σ can be realized as the Abresch-Rosenberg holomorphic differential of some, and generically infinitely many, complete surfaces with H = 1/2 in H2 × R. A similar result applies to minimal surfaces in the Heisenberg group Nil3. Finally, we classify all complete minimal vertical graphs in H2 × R. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | MTM2004-00160
MTM2004-02746 |
Cita | Fernández Delgado, I. y Mira, P. (2007). Harmonic maps and constant mean curvature surfaces in H 2 x R. American Journal of Mathematics, 129 (4), 1145-1181. |
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