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On the construction of constant mean curvature imbeddings of exotic and/or knotted spheres intoS n (1)

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References

  1. Alexandrov, A.D.: Uniqueness theorems for surfaces in the largeV. Vestnik Leningrad Univ.13, 5–8 (1958)

    Google Scholar 

  2. Alexandrov, A.D.: A characteristic property of spheres. Ann. Mat. Pura Appl.58, 303–315 (1962)

    Google Scholar 

  3. Back, A., DoCarmo, M., Hsiang, W. Y.: On fundamental equations of equivariant differential geometry, Mimeo, Univ. of Calif., Berkeley

  4. Bolza, O.: Calculus of Variation. New York: Chelsea 1960

    Google Scholar 

  5. Brieskorn, E.: Beispiele zur Differential-Topologie von Singularitäten. Invent. Math.2, 1–14 (1966)

    Google Scholar 

  6. Browder, W.: The Kervaire invariant of framed manifolds and its generalization. Ann. Math.90, 157–186 (1969)

    Google Scholar 

  7. Chern, S.S.: Differential geometry, its past and its future. Actes, Cong. Intern. Math. Tome1, 41–53 (1970)

    Google Scholar 

  8. Haefliger, A.: Knotted (4k−1) spheres in 6k-space. Ann. Math.75, 452–466 (1962)

    Google Scholar 

  9. Hopf, H.: Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Math. Nachr.4, 232–249 (1950-51)

    Google Scholar 

  10. Hsiang, W.C., Hsiang, W.Y.: On compact subgroups of the diffeomorphism groups of Kervaire spheres. Ann. Math.85, 359–369 (1967)

    Google Scholar 

  11. Hsiang, W.T., Hsiang, W.Y.: On the existence of codimension one minima spheres in compact symmetric spaces of rank 2, II. J. Differ. Geom.17, 583–594 (1982)

    Google Scholar 

  12. Hsiang, W.T., Hsiang, W.Y., Sterling, I.: On the construction of codimension two minimal immersions of exotic spheres into euclidean spheres. Bulletin AMS (In press)

  13. Hsiang, W.Y.: Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces, I: J. Differ. Geom.17, 337–356 (1982)

    Google Scholar 

  14. Hsiang, W.Y., Huynh, H.L.: Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces, II. Mimeo at Univ. of Calif., Berkeley (In press)

  15. Hsiang, W.Y., Teng, Z.H., Yu, W.C.: New examples of constant mean curvature immersions of (2k−1)-spheres into euclidean 2k-space. Ann. Math.117, 609–625 (1983)

    Google Scholar 

  16. Hsiang, W.Y.: On the bound of the dimensions of isometry groups of all possible riemannian metrics on an exotic sphere. Ann. Math.85, 351–358 (1967)

    Google Scholar 

  17. Hsiang, W.Y.: Minimal cones and the spherical Bernstein problem, I. Ann. Math.118, 61–73 (1983); II: Invent. Math.74, 351–369 (1983)

    Google Scholar 

  18. Kervaire, M.: A manifold which does not admit any differentiable structure. Comment. Math. Helv.34, 257–270 (1960)

    Google Scholar 

  19. Kervaire, M., Milnor, J.: Groups of homotopy spheres, I. Ann. Math.77, 504–537 (1963)

    Google Scholar 

  20. Levine, J.: A classification of differentiable knots. Ann. Math.82, 15–50 (1965)

    Google Scholar 

  21. Milnor, J.: On manifolds homeomorphic to the 7-sphere. Ann. Math.64, 399–405 (1956)

    Google Scholar 

  22. Schwarz, J.: Smooth functions invariant under the action of a compact Lie group. Topology14, 63–68 (1975)

    Google Scholar 

  23. Sterling, I.: New examples of imbedded spherical soap bubbles inS n(1). Thesis, University of California, Berkeley 1985

    Google Scholar 

  24. Wente, H.: Counterexample to a conjecture of H. Hopf. Mimeo, preprint. Dept. Math., University of Toledo, Toledo, Ohio

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Hsiang, Wt., Hsiang, W.y. On the construction of constant mean curvature imbeddings of exotic and/or knotted spheres intoS n (1). Invent Math 82, 423–445 (1985). https://doi.org/10.1007/BF01388863

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