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...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/93403 |
| Online Access: | https://hdl.handle.net/11441/93403 https://doi.org/10.4171/CMH/272 |
| Access Level: | Open access |
| Keyword: | Complete minimal surfaces Harmonic functions on Riemann surfaces Gauss map Holomorphic immersion |
| Summary: | 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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