Biharmonic Maps and Laguerre Minimal Surfaces
A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface Φ is its associated surface Ψ=1+u2Φ, where u lies in the unit disk. In this paper, the projection of the surface Ψ associated to a Laguerre minimal surface is shown to b...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/843156 |
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| author | Yusuf Abu Muhanna Rosihan M. Ali |
| author_facet | Yusuf Abu Muhanna Rosihan M. Ali |
| author_sort | Yusuf Abu Muhanna |
| collection | DOAJ |
| description | A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface Φ is its associated surface Ψ=1+u2Φ, where u lies in the unit disk. In this paper, the projection of the surface Ψ associated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization of Ψ is obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived for Ψ to be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given. |
| format | Article |
| id | doaj-art-1658a27c69864d7d843dc917b284de71 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1658a27c69864d7d843dc917b284de712025-02-03T06:13:22ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/843156843156Biharmonic Maps and Laguerre Minimal SurfacesYusuf Abu Muhanna0Rosihan M. Ali1Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, UAESchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaA Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surface Φ is its associated surface Ψ=1+u2Φ, where u lies in the unit disk. In this paper, the projection of the surface Ψ associated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization of Ψ is obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived for Ψ to be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.http://dx.doi.org/10.1155/2013/843156 |
| spellingShingle | Yusuf Abu Muhanna Rosihan M. Ali Biharmonic Maps and Laguerre Minimal Surfaces Abstract and Applied Analysis |
| title | Biharmonic Maps and Laguerre Minimal Surfaces |
| title_full | Biharmonic Maps and Laguerre Minimal Surfaces |
| title_fullStr | Biharmonic Maps and Laguerre Minimal Surfaces |
| title_full_unstemmed | Biharmonic Maps and Laguerre Minimal Surfaces |
| title_short | Biharmonic Maps and Laguerre Minimal Surfaces |
| title_sort | biharmonic maps and laguerre minimal surfaces |
| url | http://dx.doi.org/10.1155/2013/843156 |
| work_keys_str_mv | AT yusufabumuhanna biharmonicmapsandlaguerreminimalsurfaces AT rosihanmali biharmonicmapsandlaguerreminimalsurfaces |