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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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
  • V. I. Arnol′d and A. Avez, Ergodic problems of classical mechanics, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Translated from the French by A. Avez. MR 0232910
  • W. Blaschke, Kreis and Kugel, Viet, Leipzig, 1916; reprint, Chelsea, New York, 1949. MR 17, 887. T. Bonnesen and W. Fenchel, Theorie der Konvexer Körper, Springer, Berlin, 1934; reprint, Chelsea, New York, 1948.
  • Harley Flanders, Differential forms with applications to the physical sciences, Academic Press, New York-London, 1963. MR 0162198
  • Robert Hermann, Differential geometry and the calculus of variations, Mathematics in Science and Engineering, Vol. 49, Academic Press, New York-London, 1968. MR 0233313
  • Dimitri Koutroufiotis, Ovaloids which are almost spheres, Comm. Pure Appl. Math. 24 (1971), 289–300. MR 282318, DOI 10.1002/cpa.3160240302
  • Heinrich Liebmann, Ueber die Verbiegung der geschlossenen Flächen positiver Krümmung, Math. Ann. 53 (1900), no. 1-2, 81–112 (German). MR 1511083, DOI 10.1007/BF01456030
  • A. V. Pogorelov, Extrinsic geometry of convex surfaces, Translations of Mathematical Monographs, Vol. 35, American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by Israel Program for Scientific Translations. MR 0346714, DOI 10.1090/mmono/035
  • Ju. A. Volkov, Stability of the solution of Minkowski’s problem, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom 18 (1963), no. 1, 33–43 (Russian, with English summary). MR 0146738
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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