Position of compact hypersurfaces of the $n$-sphere
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- by James R. Wason PDF
- Proc. Amer. Math. Soc. 68 (1978), 90-91 Request permission
Abstract:
Let ${S^n}$ be the Euclidean sphere of dimension n. Let p and q be antipodal points on ${S^n}$, and, for nonnegative h, let $C(p,h),\;C(q,h)$ be the hyperspheres of constant mean curvature h centered at p and q, respectively. Then any closed hypersurface in ${S^n}$ with mean curvature bounded by h must have a point in the ’tropical’ region bounded by $C(p,h)$ and $C(q,h)$.References
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
- H. Blaine Lawson Jr., The global behavior of minimal surfaces in $S^{n}$, Ann. of Math. (2) 92 (1970), 224–237. MR 270279, DOI 10.2307/1970835
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 90-91
- MSC: Primary 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1978-0475593-7
- MathSciNet review: 475593