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Some remarks on complete simply connected minimal surfaces meeting the planes x3 = Constant Transversally |
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| Authors: | Lucio Rodríguez Harold Rosenberg |
| Affiliation: | (1) Instituto de Mathemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460 Rio de Janeiro, Brazil;(2) Departement de Mathématiques, Université de Paris VII, 2 Place Jussieu, 75251 Paris, Cedex 05, France |
| Abstract: | The helicoid and plane are the only known complete embedded minimal surfaces inR 3 that are simply connected. We prove the helicoid and plane are the only surfaces of this type that have bounded curvature and meet each plane x3 = constant in (at most) one smooth connected curve. |
| Keywords: | KeywordHeading" >Math Subject Classification 53A10 30D35 30D40 |
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