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Proceedings of the American Mathematical Society

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



Position of compact hypersurfaces of the $ n$-sphere

Author: James R. Wason
Journal: Proc. Amer. Math. Soc. 68 (1978), 90-91
MSC: Primary 53C40
MathSciNet review: 475593
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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 [Enhancements On Off] (What's this?)

  • [1] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Interscience, New York, 1963. MR 0152974 (27:2945)
  • [2] H. B. Lawson, Jr., The global behavior of minimal surfaces in $ {S^n}$, Ann. of Math. (2) 92 (1970), 224-237. MR 0270279 (42:5169)

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Article copyright: © Copyright 1978 American Mathematical Society

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