Minimal Disks and Compact Hypersurfaces in Euclidean Space

Let Mnbe a smooth connected compact hypersurface in (n + 1)-dimensional Euclidean space En + 1, let An + 1be the unbounded component of En + 1- Mn, and let κ1⩽ κ2⩽ ⋯ ⩽ κnbe the principal curvatures of Mnwith respect to the unit normal pointing into An + 1. It is proven that if $\kappa_2 + \cdots + \...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1985-01, Vol.94 (2), p.321-328
Main Authors: Moore, John Douglas, Schulte, Thomas
Format: Article
Language:English
Subjects:
Connected regions
Curvature
Euclidean space
Hypersurfaces
Mathematical manifolds
Mathematical theorems
Minimal surfaces
Simply connected regions
Tangents
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Summary:Let Mnbe a smooth connected compact hypersurface in (n + 1)-dimensional Euclidean space En + 1, let An + 1be the unbounded component of En + 1- Mn, and let κ1⩽ κ2⩽ ⋯ ⩽ κnbe the principal curvatures of Mnwith respect to the unit normal pointing into An + 1. It is proven that if $\kappa_2 + \cdots + \kappa_n < 0$, then An + 1is simply connected.
ISSN:0002-9939
1088-6826
DOI:10.1090/s0002-9939-1985-0784186-7