## Minimal disks and compact hypersurfaces in Euclidean space

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- by John Douglas Moore and Thomas Schulte
- Proc. Amer. Math. Soc.
**94**(1985), 321-328 - DOI: https://doi.org/10.1090/S0002-9939-1985-0784186-7
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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.## References

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## Bibliographic Information

- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**94**(1985), 321-328 - MSC: Primary 53C40; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784186-7
- MathSciNet review: 784186