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Minimal Surfaces in a Cone

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Abstract

We prove the convex hull property for properly immersed minimal hypersurfaces in a cone of ℝn. We deal with the existence of new barriers for the maximum principle application in noncompact truncated tetrahedral domains of ℝ3, describing the space of such domainsadmitting barriers of this kind. Nonexistence results for nonflatminimal surfaces whose boundary lies in opposite faces of a tetrahedraldomain are obtained. Finally, new simple closed subsets of ℝ3 whichhave the property of intersecting any properly immersed minimal surfaceare shown.

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  1. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Francisco J. López

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  1. Francisco J. López
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López, F.J. Minimal Surfaces in a Cone. Annals of Global Analysis and Geometry 20, 253–299 (2001). https://doi.org/10.1023/A:1012451110396

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  • DOI: https://doi.org/10.1023/A:1012451110396

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