Journal of Differential Geometry

Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. I

Wu-yi Hsiang

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 17, Number 2 (1982), 337-356.

Dates
First available in Project Euclid: 25 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214436924

Digital Object Identifier
doi:10.4310/jdg/1214436924

Mathematical Reviews number (MathSciNet)
MR664499

Zentralblatt MATH identifier
0493.53043

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Hsiang, Wu-yi. Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. I. J. Differential Geom. 17 (1982), no. 2, 337--356. doi:10.4310/jdg/1214436924. https://projecteuclid.org/euclid.jdg/1214436924


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References

  • [1] A. D. Alexandrov, A characteristic property of spheres, Ann. Mat. Pura Appl. (4) 58 (1962) 303-315.
  • [2] E. Bombieri, E. DeGiorgi and E. Guisti, Minimal cones and the Bernstein problem, Invent. Math. 7 (1969) 243-268.
  • [3] C. Delaunay, Sur la surface de revolution dont la courbure mayenne est constant, J. Math. Pures Appl. (1) 6 (1841) 309-320.
  • [4] H. Hopf, Uber Flachenmit einer Relation zwischen den Hauptkrummerngen, Math. Nachr. 4 (1950-51) 232-249.
  • [5] W. Y. Hsiang and W. T. Hsiang, On the existence of codimension one minimal spheres in compact symmetric spaces of rank 2. II, J. Differential Geometry 17 (1982).
  • [6] W. Y. Hsiang and B. Lawson, Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971) 1-38.
  • [7] W. Y. Hsiang, Z. H. Teng and W. C. Yu, New examples of constant mean curvature immersions of S3 into E4, Proc. Nat. Acad. Sci. U.S.A., to appear.
  • [8] W. Y. Hsiang, Z. H. Teng and W. C. Yu, New examples of constant mean curvature immersions of (2k --)-spheres into euclidean 2k space, to appear.
  • [9] W. Y. Hsiang and W. C. Yu, A generalization of a theorem of Delaunay, J. Differential Geometry 16 (1981) 161-177.
  • [10] A Back, M. DoCarmo and W. Y. Hsiang, Fundamental equations in equivariant Riemannian geometry, to appear.
  • [11] W. Y. Hsiang, On generalization of theorems A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature, to appear.
  • [12] W. Y. Hsiang, Minimal hypersurfaces of generalized rotational types, to appear.

See also

  • Part II: Wu-yi Hsiang, , Hsueh-Ling Huynh. Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. II. Pacific J. Math. ,Volume 130, Number 1 (1987), 75--95.