References
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
Alexandrov, A.D.: A characteristic property of spheres. Ann. Mat. Pura Appl.58, 303–315 (1962)
Cartan, É.: Sur une classe remarquable d'espaces de Riemann. Bull. Soc. Math. Fr.54, 214–264 (1926);55, 114–134 (1927)
Cartan, É.: La géométrie des gropues de transformations. J. Math. Pures Appl.6, 1–119 (1927)
Federer, H.: Geometric measure theory. Berlin Heidelberg New York: Springer 1969
Gidas, B., Ni, W., Nirenberg, L.: Symmetry and related properties via the maximal principle. Comm. Math. Physics68, 209–243 (1979)
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, 2nd edition, Berlin Heidelberg New York: Springer 1983
Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York: Academic Press 1978
Hopf, H.: Differential geometry in the large (Lecture Notes Stanford 1956), (Lect. Notes Math., vol. 1000), Berlin Heidelberg New York: Springer 1983
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)
Hsiang, W.Y.: Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces, I. J. Differ. Geom.17, 337–356 (1982)
Hsiang, W.Y., Huyng, H.L.: On spherical soap bubble in non-compact symmetric spaces of rank ≦2 (to appear)
Schmidt, E.: Beweis der isomerimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl. Math. Z.44, 1–109 (1939)
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)
Simons, J.: Minimal varieties in Riemannian manifolds. Ann. Math.88, 62–105 (1968)
Wente, H.: Counterexample to a conjecture of H. Hopf. Pac. J. Math.121, 193–243 (1986)
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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
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DOI: https://doi.org/10.1007/BF01388843