Skip to main content
Log in

On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces, I

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Alexandrov, A.D.: Uniqueness theorems for surfaces in the large, V. Vestnik Leningrad Univ.13, 5–8 (1958); Am. Math. Soc. Trans. (Series 2)21, 412–416

    Google Scholar 

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

    Google Scholar 

  3. Cartan, É.: Sur une classe remarquable d'espaces de Riemann. Bull. Soc. Math. Fr.54, 214–264 (1926);55, 114–134 (1927)

    Google Scholar 

  4. Cartan, É.: La géométrie des gropues de transformations. J. Math. Pures Appl.6, 1–119 (1927)

    Google Scholar 

  5. Federer, H.: Geometric measure theory. Berlin Heidelberg New York: Springer 1969

    Google Scholar 

  6. Gidas, B., Ni, W., Nirenberg, L.: Symmetry and related properties via the maximal principle. Comm. Math. Physics68, 209–243 (1979)

    Google Scholar 

  7. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, 2nd edition, Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  8. Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York: Academic Press 1978

    Google Scholar 

  9. Hopf, H.: Differential geometry in the large (Lecture Notes Stanford 1956), (Lect. Notes Math., vol. 1000), Berlin Heidelberg New York: Springer 1983

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. Hsiang, W.Y., Huyng, H.L.: On spherical soap bubble in non-compact symmetric spaces of rank ≦2 (to appear)

  13. Schmidt, E.: Beweis der isomerimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl. Math. Z.44, 1–109 (1939)

    Google Scholar 

  14. Schmidt, E.: Der Brun-Minkowskische Satz und ein Spiegel-theorem sowie die isoperimetrische Eigenschaft der Kugeln in der euklidischen und hyperbolischen Geometrie. Math. Ann.120, 307–429 (1947–49)

    Google Scholar 

  15. Simons, J.: Minimal varieties in Riemannian manifolds. Ann. Math.88, 62–105 (1968)

    Google Scholar 

  16. Wente, H.: Counterexample to a conjecture of H. Hopf. Pac. J. Math.121, 193–243 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hsiang, WT., Hsiang, Wy. On the uniqueness of isoperimetric solutions and imbedded soap bubbles in non-compact symmetric spaces, I. Invent Math 98, 39–58 (1989). https://doi.org/10.1007/BF01388843

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388843

Keywords

Navigation