Duke Mathematical Journal

On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature

Wu-Yi Hsiang

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Article information

Source
Duke Math. J., Volume 49, Number 3 (1982), 485-496.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077315376

Digital Object Identifier
doi:10.1215/S0012-7094-82-04927-4

Mathematical Reviews number (MathSciNet)
MR672494

Zentralblatt MATH identifier
0496.53006

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Hsiang, Wu-Yi. On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature. Duke Math. J. 49 (1982), no. 3, 485--496. doi:10.1215/S0012-7094-82-04927-4. https://projecteuclid.org/euclid.dmj/1077315376


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References

  • [1] A. D. Aleksandrov, Uniqueness theorems for surfaces in the large. V, Amer. Math. Soc. Transl. (2) 21 (1962), 412–416.
  • [2] A. D. Alexandrov, A characteristic property of spheres, Ann. Mat. Pura Appl. (4) 58 (1962), 303–315.
  • [3] C. Delaunay, Sur le surface de révolution dont la courbure mayenne est constante, J. Math. Pures. Appl. Ser. 1 6 (1841), 309–320.
  • [4] H. Hopf, Über Flächen mit einer Relation zwischen den Hauptkrümmungen, Math. Nachr. 4 (1951), 232–249.
  • [5] W. Y. Hsiang and W. T. Hsiang, On the construction of exotic and/or knotted spheres of constant mean curvature in the standard sphere, to appear.
  • [6] W. Y. Hsiang and B. Lawson, Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1–38.
  • [7] W. Y. Hsiang and W. Yu, A generalization of Delaunay theorem on the construction of rotational symmetric hypersurfaces of constant mean curvature and harmonic maps, (to appear in J. of Diff. Geo.).
  • [8] H. Liebmann, Über die Verbiegung der geschlossenen Flächen positier Krümmung, Math. Ann. 53 (1900), 81–112.