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The structure of an infinite, complete, convex hypersurface inE 4 with bounded mean curvature

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Abstract

The following theorem is proved.

THEOREM. If on an infinite, complete, convex hypersurface F in E4 the mean curvature is 1 − ε ≤ H ≤ 1, where 0 ≤ ε ≤ 10−11, then F is a cylindrical hypersurface.

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References

  1. S. J. Cheng and S. T. Yau, "Differential equations on Riemannian manifolds and their geometric applications," Comm. Pure Appl. Math.,28 No. 3, 333–354 (1975).

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  2. A. V. Pogorelov, "The mean curvature of an infinite complete convex surface," Dokl. Akad. Nauk SSSR,197 No. 4, 788–789 (1971).

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  3. V. I. Diskant, "Convex surfaces with bounded mean curvature," Sib. Mat. Zh.,12 No. 3, 659–663 (1971).

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Authors
  1. A. A. Borisenko
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  2. L. N. Sergienko
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Additional information

Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 8–9, 1991.

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Borisenko, A.A., Sergienko, L.N. The structure of an infinite, complete, convex hypersurface inE 4 with bounded mean curvature. J Math Sci 69, 829–830 (1994). https://doi.org/10.1007/BF01250809

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  • DOI: https://doi.org/10.1007/BF01250809

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