Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces

被引：1

作者：

Jleli, Mohamed ^{[1
]}

机构：

[1] King Saud Univ, Dept Math, Riyadh 11451, Saudi Arabia

来源：

ADVANCED NONLINEAR STUDIES | 2009年 / 9卷 / 02期

关键词：

Mean curvature; Hypersurface; Bifurcation; EUCLIDEAN; 3-SPACE; MODULI SPACE; SURFACES; BIFURCATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the existence of constant mean curvature hypersurfaces which are cylindrically bounded and which bifurcate from the family of immersed constant mean curvature hypersurface of revolution. Based on the study of the spectrum of the Jacobi operator (the linearized mean curvature) about this family, the existence of new branches follows from a bifurcation result of Crandall and Rabinowitz.

引用

页码：243 / 261

页数：19

共 22 条

[1] [Anonymous], 1994, GRUNDLEHREN MATH WIS
[2] [Anonymous], 2002, TOPOLOGY GEOMETRY CO
[3] BRYANT RL, 1987, ASTERISQUE, V154
[4] CRANDALL MG, 1973, ARCH RATION MECH AN, V52, P161, DOI 10.1007/BF00282325
[5] Delaunay C., 1841, J. Math. Pures Appl, V6, P309
[6] NEW SURFACES OF CONSTANT MEAN-CURVATURE
GROSSEBRAUCKMANN, K
[J]. MATHEMATISCHE ZEITSCHRIFT, 1993, 214 (04) : 527 - 565
[7] HISIANG WY, 1981, J DIFFER GEOM, V16, P161
[8] An end-to-end construction for compact constant mean curvature surfaces
Jleli, M
Pacard, F
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2005, 221 (01) : 81 - 108
[9] Jleli M, 2009, ADV NONLINEAR STUD, V9, P29
[10] COMPLETE CONSTANT MEAN-CURVATURE SURFACES IN EUCLIDEAN 3-SPACE
KAPOULEAS, N
[J]. ANNALS OF MATHEMATICS, 1990, 131 (02) : 239 - 330

← 1 2 3 →