RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE

RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE

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摘要 In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere. In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.

作者王静张银山

机构地区 School of Mathematics and Statistics School of Mathematics and Statistics

出处《Acta Mathematica Scientia》 SCIE CSCD 2016年第6期1609-1618,共10页 数学物理学报（B辑英文版）

基金 supported by NSFC(11371330)

关键词 homogeneous 3-manifolds Berger sphere constant mean curvature surface Hopf torus Clifford torus homogeneous 3-manifolds Berger sphere constant mean curvature surface Hopf torus Clifford torus

分类号 O186.1 [理学—基础数学]

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1Mohamed JLELI.STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE[J].Acta Mathematica Scientia,2013,33(3):830-838. 被引量：1

二级参考文献16

1Barbosa J L, Gomes J, Silveira A. Foliation of 3-dimentional space forms by surfaces with constant mean curvature. Bol Soc Bras Math, 1987, 18: 1-12.
2Berard P, Lopes de Lima L, Rossman W. Index growth of hypersurfaces with constant mean curvature. Mathematische Zeitschrift, 2002, 239(1): 99-115.
3Bryant R L. Surfaces of mean curvature one in hyperbolic space. Theorie des varietes minimales et applications, Asterisque, 1987, 154/155: 341-347.
4Do Carmo M. Riemannian Geometry. Bosten: Birkhauser, 1992.
5Jleli M. Moduli space theory of constant mean curvature hypersurfaces. Journal of Advanced Nonlinear Studies. 2009, 9(1): 29-68.
6Jleli M. Symmetry breaking of immersed constant mean curvature hypersurfaces. Advanced Nonlinear Studies, 2009, 9: 129-147.
7Jleli M. Stability results of rotationally constant mean curvature surfaces in hyperbolic space. Colloq Math, 2012, 126: 269-280.
8Jleli M. Bifurcations of constant mean curvature surfaces of revolution in hyperbolic space (To appear).
9Korevaar N, Kusner R, Meeks W, Solomon B. Constant mean curvature surfaces in hyperbolic space. American, J Maths, 1992, 114: 1-43.
10Kusner R, Mazzeo R, Pollack D. The moduli spaces of complete embeeded constant mean curvature surfaces. Geom Funet Anal, 1996, 6: 120-137.

1陈行堤.可逆调和映照与最小曲面[J].泉州师范学院学报,2009,27(6):1-5.
2宋鸿藻,胡泽军,等.Hypersurfaces with Constant Mean Curvature in Space Forms[J].Chinese Quarterly Journal of Mathematics,1996,11(1):42-48.
3邓勤涛.COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES[J].Acta Mathematica Scientia,2011,31(1):353-360. 被引量：1
4XuSenlin,DengQintao,ChenDongmei.THE SPECTRUM OF COMPACT HYPERSURFACE IN SPHERE[J].Analysis in Theory and Applications,2004,20(3):288-293.
5罗秀华,张光照,邢家省.固定边界的曲面中面积最小曲面的必要条件[J].河南科学,2015,33(10):1691-1695.
6王振东.多彩斑斓诚可爱——漫话肥皂泡[J].力学与实践,2014,36(4):511-516. 被引量：2
7Hu Zejun Li Haizhong Hu Zejun Department of Mathematics Zhengzhou University Zhengzhou,450052 ChinaLi Haizhong Department of Applied Mathematics Tsinghua University Beijing,100084 China.A Global Pinching Theorem for Compact Surfaces in S^3 with Constant Mean Curvature[J].Acta Mathematica Sinica,English Series,1996,12(2):126-132.
8苏变萍,舒世昌,Yi Annie Han.HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE[J].Acta Mathematica Scientia,2011,31(3):1091-1102. 被引量：1
9FU Hai-ping,XU Hong-wei.Weakly stable constant mean curvature hypersurfaces[J].Applied Mathematics(A Journal of Chinese Universities),2009,24(1):119-126.
10Yi Bing SHEN,Xiao Hua ZHU.On Complete Hypersurfaces with Constant Mean Curvature and Finite L^p-norm Curvature in R^(n+1)[J].Acta Mathematica Sinica,English Series,2005,21(3):631-642.

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RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE

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