SO(2)-invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces

1995 ◽  
Vol 87 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Renzo Caddeo ◽  
Paola Piu ◽  
Andrea Ratto
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Homogeneous Spaces ◽  
Constant Mean Curvature Surfaces ◽  
3 Dimensional

scholarly journals On Bernstein–Heinz–Chern–Flanders inequalities

2008 ◽  
Vol 144 (2) ◽  
pp. 457-464 ◽  
Author(s):  
J. L. M. BARBOSA ◽  
G. P. BESSA ◽  
J. F. MONTENEGRO
Keyword(s):  
Lower Bounds ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Point Of View ◽  
Constant Mean Curvature Surfaces ◽  
3 Dimensional ◽  
Codimension One ◽  
Simple Curves

AbstractWe give an interpretation of the Chern–Heinz inequalities for graphs in order to extend them to transversally oriented codimension one C2-foliations of Riemannian manifolds. It contains Salavessa's work on mean curvature of graphs and fully generalizes results of Barbosa–Kenmotsu–Oshikiri [3] and Barbosa–Gomes–Silveira [2] about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. This point of view of the Chern–Heinz inequalities can be applied to prove a Haymann–Makai–Osserman inequality (lower bounds of the fundamental tones of bounded open subsets Ω ⊂ ℝ2 in terms of its inradius) for embedded tubular neighbourhoods of simple curves of ℝn.

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