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ON MINIMAL SURFACES SATISFYING THE OMORI–YAU PRINCIPLE

Part of: Global differential geometry

Published online by Cambridge University Press:  16 June 2011

ALBERT BORBÉLY
ALBERT BORBÉLY*
Affiliation:
Department of Mathematics, Faculty of Science, Kuwait University, PO Box 5969, Safat 13060, Kuwait (email: [email protected])
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Abstract

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Complete minimal immersions satisfying the Omori–Yau maximum principle are investigated. It is shown that the limit set of a proper immersion into a convex set must be the whole boundary of the convex set. In case of a nonproper and nonplanar immersion we prove that the convex hull of the immersion is a half-space or ℝ3.

Keywords

minimal surfaceOmori–Yau maximum principle

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 33 - 39
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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