Stable constant mean curvature hypersurfaces in some Riemannian manifolds

Commentarii Mathematici Helvetici

Volumn 73, Issue 4, 1998, Pages 584-602

  Montiel, Sebastián ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Constant mean curvature; Hypersurface; Stability

Indexed keywords

EID: 0032426317     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000140050070     Document Type: Article

References (22)

1. A.D. Alexandrov, Uniqueness theorems for surfaces in the large I, Vestnik Leningrad Univ. 11 (1956), 5-17.
2. J.L. Barbosa and M.P. do Carmo, Stability of hypersurfaces with constant mean cuvature, Math. Z. 185 (1984), 339-353.
3. J.L. Barbosa, M.P. do Carmo and J. Eschenburg, Stability of hypersurfaces with constant mean curvature in Riemannian manifolds, Math. Z. 197 (1988), 123-138.
4. R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49.
5. I. Bivens, Integral formulas and hyperspheres in a simply connected space form, Trans. Amer. Math. Soc. 88 (1983), 113-118.
6. J. Choe and R. Gulliver, Isoperimetric inequalities on minimal submanifolds of space forms, Manuscripta Math. 77 (1992), 169-189.
7. A. El Soufi and S. Ilias, Majoration de la seconde valeur propre d'un operateur de Schrödinger sur une variété compacte et applications, J. Funct. Anal. 103 (1992), 294-316.
8. 1, Math. Ann. 280 (1988), 389-402.
9. J.J. Jellett, Sur la surface dont la courbure moyenne est constante, J. Math. Pures Appl. 18 (1853), 163-167.
10. M. Kanai, On a differential equation characterizing a Riemannian structure on a manifold, Tokyo J. Math. 6 (1983), 143-151.
11. A. Lichnerowicz, Géométrie des Groupes des Transformations, Dunod, Paris, 1958.
12. H. Liebmann, Eine neue Eigenschaft der Kugel, Nachr. Kg. Ges. Wiss. Götingen, Math. Phys. Kl. (1899), 44-55.
13. S. Montiel, Unicity of constant mean curvature hypersurfaces in foliated Riemannian manifolds, preprint.
14. S. Montiel and A. Ros, Compact hypersurfaces: the Alexandrov theorem for higher order mean curvatures, pp. 279-296. In: B. Lawson and K. Tenenblat (Eds.): Pitman Monographs and Surveys, in honor to M. P. Carmo, Pure and Applied Mathematics 52 (1991).
15. M. Obata, Conformal transformations of Riemannian manifolds, J. Diff. Geom. 4 (1970), 311-333.
16. B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York 1983.
17. M. Ritoré and A. Ros, Stable constant mean curvature tori and the isoperimetric problem in three space forms, Comment. Math. Helv. 67 (1992), 293-305.
18. M. Ritoré and A. Ros, The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds, Trans. Amer. Math. Soc. 348 (1996), 391-410.
19. n with conformal Maslov form and the Whitney sphere, J. Math. Soc. Japan. 50 (1) (1998), 203-226.
20. S. Tanno and W. Weber, Closed conformal vector fields, J. Diff. Geom. 3 (1969), 361-366.
21. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251-275.
22. S.T. Yau, Isoperimetric constants and the first eigenvalue of a compact manifold, Ann. Sci. Ecole Norm. Sup. 8 (1975), 487-507.