constant mean curvature hypersurfaces
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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 ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE

2019 ◽  
Vol 101 (2) ◽  
pp. 333-338
Author(s):  
JULIEN ROTH ◽  
ABHITOSH UPADHYAY
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Small Ball ◽  
Constant Mean Curvature Hypersurfaces ◽  
Geodesic Spheres

We show that almost stable constant mean curvature hypersurfaces contained in a sufficiently small ball of a manifold of bounded sectional curvature are close to geodesic spheres.

Minimal hypersurfaces in ℝn × Sm

2019 ◽  
Vol 19 (1) ◽  
pp. 1-13
Author(s):  
Jimmy Petean ◽  
Juan Miguel Ruiz
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Minimal Hypersurfaces ◽  
Constant Mean Curvature Hypersurfaces

Abstract We classify minimal hypersurfaces in ℝn × Sm with n, m ≥ 2 which are invariant by the canonical action of O(n) × O(m). We also construct compact and noncompact examples of invariant hypersurfaces of constant mean curvature. We show that the minimal hypersurfaces and the noncompact constant mean curvature hypersurfaces are all unstable.

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