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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Almost spherical convex hypersurfaces


Author: John Douglas Moore
Journal: Trans. Amer. Math. Soc. 180 (1973), 347-358
MSC: Primary 53C45
MathSciNet review: 0320964
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Abstract: Let $ M$ be a smooth compact hypersurface with positive sectional curvatures in $ n$-dimensional euclidean space. This paper gives a sufficient condition for $ M$ to lie in the spherical shell bounded by concentric spheres of radius $ 1 - \epsilon $ and $ 1 + \epsilon $. This condition is satisfied, in the case where $ n = 3$, if the Gaussian curvature or the mean curvature of $ M$ is sufficiently pointwise close to one.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0320964-2
PII: S 0002-9947(1973)0320964-2
Keywords: Ovaloid, convex hypersurface, almost spherical hypersurface, integral formulae of Minkowski
Article copyright: © Copyright 1973 American Mathematical Society