A non-existence theorem for stable constant mean curvature hypersurfaces

1991 ◽  
Vol 70 (1) ◽  
pp. 219-226 ◽  
Author(s):  
Leung-Fu Cheung
Keyword(s):  
Existence Theorem ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces

scholarly journals Gauss map and the topology of constant mean curvature hypersurfaces of $$\mathbb {S}^{7}$$ and $$\mathbb {CP}^{3}$$

2019 ◽  
Vol 163 (1-2) ◽  
pp. 279-290
Author(s):  
Fidelis Bittencourt ◽  
Pedro Fusieger ◽  
Eduardo R. Longa ◽  
Jaime Ripoll
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Constant Mean Curvature Hypersurfaces

scholarly journals Stable constant mean curvature hypersurfaces

2007 ◽  
Vol 135 (10) ◽  
pp. 3359-3367 ◽  
Author(s):  
Maria Fernanda Elbert ◽  
Barbara Nelli ◽  
Harold Rosenberg
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces

scholarly journals The structure of weakly stable constant mean curvature hypersurfaces

2008 ◽  
Vol 60 (1) ◽  
pp. 101-121 ◽  
Author(s):  
Xu Cheng ◽  
Leung-fu Cheung ◽  
Detang Zhou
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces ◽  
Weakly Stable

Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Mohamed Jleli
Keyword(s):  
Symmetry Breaking ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Jacobi Operator ◽  
Constant Mean Curvature Hypersurfaces ◽  
The Family ◽  
Constant Mean Curvature Hypersurface ◽  
Curvature Hypersurface

AbstractIn 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.

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