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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Minimal disks and compact hypersurfaces in Euclidean space

Authors: John Douglas Moore and Thomas Schulte
Journal: Proc. Amer. Math. Soc. 94 (1985), 321-328
MSC: Primary 53C40; Secondary 53C42
MathSciNet review: 784186
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Abstract: Let $ {M^n}$ be a smooth connected compact hypersurface in $ (n + 1)$-dimensional Euclidean space $ {E^{n + 1}}$, let $ {A^{n + 1}}$ be the unbounded component of $ {E^{n + 1}} - {M^n}$, and let $ {\kappa _1} \leqslant {\kappa _2} \leqslant \cdots \leqslant {\kappa _n}$ be the principal curvatures of $ {M^n}$ with respect to the unit normal pointing into $ {A^{n + 1}}$. It is proven that if $ {\kappa _2} + \cdots + {\kappa _n} < 0$, then $ {A^{n + 1}}$ is simply connected.

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