Complete minimal surfaces and harmonic functions
We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/93403 |
| Acceso en línea: | https://hdl.handle.net/11441/93403 https://doi.org/10.4171/CMH/272 |
| Access Level: | acceso abierto |
| Palabra clave: | Complete minimal surfaces Harmonic functions on Riemann surfaces Gauss map Holomorphic immersion |
| Sumario: | We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed. |
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