Some remarks on complete simply connected minimal surfaces meeting the planes x3 = Constant Transversally期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Some remarks on complete simply connected minimal surfaces meeting the planes x3 = Constant Transversally

Authors:	Lucio Rodríguez Harold Rosenberg

Institution:	(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:	Math Subject Classification" target="_blank">Math Subject Classification 53A10 30D35 30D40
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