Almost spherical convex hypersurfaces
Author:
John Douglas Moore
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
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Ovaloid,
convex hypersurface,
almost spherical hypersurface,
integral formulae of Minkowski
Article copyright:
© Copyright 1973
American Mathematical Society
