Almost spherical convex hypersurfaces
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- by John Douglas Moore PDF
- Trans. Amer. Math. Soc. 180 (1973), 347-358 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 180 (1973), 347-358
- MSC: Primary 53C45
- DOI: https://doi.org/10.1090/S0002-9947-1973-0320964-2
- MathSciNet review: 0320964