STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

doi:10.1016/S0252-9602(13)60042-9

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 830-838.doi: 10.1016/S0252-9602(13)60042-9

STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

Mohamed JLELI

Department of Mathematics, King Saud Unibersity, Saudi Arabia

收稿日期:2011-12-30 修回日期:2012-05-24 出版日期:2013-05-20 发布日期:2013-05-20
基金资助:
This work is supported by the King Saud University D.S.F.P program.

STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

Mohamed JLELI

Department of Mathematics, King Saud Unibersity, Saudi Arabia

Received:2011-12-30 Revised:2012-05-24 Online:2013-05-20 Published:2013-05-20
Supported by:
This work is supported by the King Saud University D.S.F.P program.

摘要/Abstract

摘要：

In this article, by solving a nonlinear differential equation, we prove the existence of a one parameter family of constant mean curvature hypersurfaces in the hyperbolic space with two ends. Then, we study the stability of these hypersurfaces.

关键词: Hypersurface, hyperbolic space, mean curvature

Abstract:

Key words: Hypersurface, hyperbolic space, mean curvature

中图分类号:

53C42

Mohamed JLELI. STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE[J]. 数学物理学报(英文版), 2013, 33(3): 830-838.

Mohamed JLELI. STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE[J]. Acta mathematica scientia,Series B, 2013, 33(3): 830-838.

参考文献

[1] Barbosa 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

[2] Berard P, Lopes de Lima L, Rossman W. Index growth of hypersurfaces with constant mean curvature. Mathematische Zeitschrift, 2002, 239(1): 99–115

[3] Bryant R L. Surfaces of mean curvature one in hyperbolic space. Th´eorie des vari´et´es minimales et appli-cations, Ast´erisque, 1987, 154/155: 341–347

[4] Do Carmo M. Riemannian Geometry. Bosten: Birkhauser, 1992

[5] Jleli M. Moduli space theory of constant mean curvature hypersurfaces. Journal of Advanced Nonlinear Studies. 2009, 9(1): 29–68

[6] Jleli M. Symmetry breaking of immersed constant mean curvature hypersurfaces. Advanced Nonlinear Studies, 2009, 9: 129–147

[7] Jleli M. Stability results of rotationally constant mean curvature surfaces in hyperbolic space. Colloq Math, 2012, 126: 269–280

[8] Jleli M. Bifurcations of constant mean curvature surfaces of revolution in hyperbolic space (To appear)

[9] Korevaar N, Kusner R, Meeks W, Solomon B. Constant mean curvature surfaces in hyperbolic space. American, J Maths, 1992, 114: 1–43

[10] Kusner R,Mazzeo R, Pollack D. The moduli spaces of complete embeeded constant mean curvature surfaces. Geom Funct Anal, 1996, 6: 120–137

[11] Lawson B. Complete minimal surfaces in S3. Ann Math, 1970, 92: 335–374

[12] Lawson B. Lectures on minimal submanifolds. Vol1. Second Ed//Mathematics Lecture Series. Vol 9.Wilmn-ington, Del, 1980

[13] Mazzeo R, Pacard F. Bifurcating nodoids//Commemorating SISTAG, Contemporary Mathematics 314. American Mathematical Society, 2002: 169–186

[14] Pacard F, Pimentel F A A. Attaching handles to constant-mean-curvature −1 surfaces in hperbolic 3-space. Jour of the Institute of Mathematics of Jussieu, 2004, 3: 421–459

[15] Rossman W, Umehara K, Yamada K. Mean curvature 1 surface with low total curvature in hyperbolic 3-space I. Hiroshima Math J, 2004, 34(1): 21–56

[16] Umehara K, Yamada K. Complete surface of constant mean curvature 1 in the hyperbolic 3-space. Ann of Math, 1993, 137: 611–638

STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	马如云, 高红亮. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN[J]. 数学物理学报(英文版), 2017, 37(5): 1472-1482.
[2]	何春蕾, 黄守军, 邢晓敏. SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW[J]. 数学物理学报(英文版), 2017, 37(3): 657-667.
[3]	王静, 张银山. RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE[J]. 数学物理学报(英文版), 2016, 36(6): 1609-1618.
[4]	Kamal OULD BOUH. EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY[J]. 数学物理学报(英文版), 2016, 36(5): 1305-1316.
[5]	邱红兵. AN ESTIMATE FOR THE MEAN CURVATURE OF SUBMANIFOLDS CONTAINED IN A HOROBALL[J]. 数学物理学报(英文版), 2013, 33(6): 1561-1570.
[6]	杨登允, 许洪伟, 付海平. NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES[J]. 数学物理学报(英文版), 2013, 33(5): 1269-1274.
[7]	Wael ABDELHEDI. CONCENTRATION OF SOLUTIONS FOR THE MEAN CURVATURE PROBLEM[J]. 数学物理学报(英文版), 2013, 33(3): 631-642.
[8]	吴加勇. SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J]. 数学物理学报(英文版), 2013, 33(1): 171-186.
[9]	谭忠, 吴国春. ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1741-1748.
[10]	黄广月, 李兴校. ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN Hⁿ(−1)[J]. 数学物理学报(英文版), 2011, 31(4): 1383-1388.
[11]	苏变萍, 舒世昌, Yi Annie Han. HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE[J]. 数学物理学报(英文版), 2011, 31(3): 1091-1102.
[12]	周家足. ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES[J]. 数学物理学报(英文版), 2011, 31(2): 361-366.
[13]	邓勤涛. COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES[J]. 数学物理学报(英文版), 2011, 31(1): 353-360.
[14]	简怀玉, 鞠红杰, 刘艳楠, 孙伟. SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS[J]. 数学物理学报(英文版), 2010, 30(6): 2006-2016.
[15]	陈旭忠, 沈一兵. A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J]. 数学物理学报(英文版), 2010, 30(4): 1053-1064.