JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SPHERE-FOLIATED MINIMAL AND CONSTANT MEAN CURVATURE HYPERSURFACES IN PRODUCT SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SPHERE-FOLIATED MINIMAL AND CONSTANT MEAN CURVATURE HYPERSURFACES IN PRODUCT SPACES
Seo, Keom-Kyo;
  PDF(new window)
 Abstract
In this paper, we prove that minimal hypersurfaces when n 3 and nonzero constant mean curvature hypersurfaces when n 2 foliated by spheres in parallel horizontal hyperplanes in must be rotationally symmetric.
 Keywords
foliation;constant mean curvature;rotationally symmetric hypersurface;product space;
 Language
English
 Cited by
 References
1.
U. Abresch and H. Rosenberg, A Hopf differential for constant mean curvature surfaces in $S^2$ ${\times}$ R and $H^2$ ${\times}$ R, Acta Math. 193 (2004), no. 2, 141-174. crossref(new window)

2.
P. Berard and R. Sa Earp, Minimal hypersurfaces in $H^n$ ${\times}$ R, total curvature and index, arXiv: 0808.3838v1.

3.
M. Cavalcante and J. de Lira, Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces, Michigan Math. J. 55 (2007), no. 1, 163-181. crossref(new window)

4.
L. Hauswirth, Minimal surfaces of Riemann type in three-dimensional product manifolds, Pacific J. Math. 224 (2006), no. 1, 91-117. crossref(new window)

5.
W.-T. Hsiang and W.-Y. Hsiang, On the uniqueness of isoperimetric solutions and imbedded soap bubbles in noncompact symmetric spaces. I, Invent. Math. 98 (1989), no. 1, 39-58. crossref(new window)

6.
W. Jagy, Minimal hypersurfaces foliated by spheres, Michigan Math. J. 38 (1991), no. 2, 255-270. crossref(new window)

7.
W. Jagy, Sphere-foliated constant mean curvature submanifolds, Rocky Mountain J. Math. 28 (1998), no. 3, 983-1015. crossref(new window)

8.
R. Lopez, Constant mean curvature hypersurfaces foliated by spheres, Differential Geom. Appl. 11 (1999), no. 3, 245-256. crossref(new window)

9.
B. Nelli and H. Rosenberg, Minimal surfaces in $H^2$ ${times}$ R, Bull. Braz. Math. Soc. (N.S.) 33 (2002), no. 2, 263-292. crossref(new window)

10.
B. Nelli, R. Sa Earp, W. Santos, and E. Toubiana, Uniqueness of H-surfaces in $H^2$ ${\times}$ R, ${\left|H\right|}$${\leq}$ 1/2, with boundary one or two parallel horizontal circles, Ann. Global Anal. Geom. 33 (2008), no. 4, 307-321. crossref(new window)

11.
S.-H. Park, Sphere-foliated minimal and constant mean curvature hypersurfaces in space forms and Lorentz-Minkowski space, Rocky Mountain J. Math. 32 (2002), no. 3, 1019-1044. crossref(new window)

12.
R. Sa Earp and E. Toubiana, Screw motion surfaces in $H^2$ ${\times}$ R and $S^2$ ${\times}$ R, Illinois J. Math. 49 (2005), no. 4, 1323-1362.

13.
S. Stahl, The Poincare Half-Plane, Jones and Bartlett Publishers, Boston, MA, 1993.