scholarly journals Triply periodic minimal and constant mean curvature surfaces

2012 ◽  
Vol 2 (5) ◽  
pp. 582-588 ◽  
Author(s):  
Karsten Grosse-Brauckmann
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Point Of View ◽  
Constant Mean Curvature Surfaces ◽  
Mathematical Point ◽  
Periodic Surfaces ◽  
Triply Periodic ◽  
General Readership

We want to summarize some established results on periodic surfaces which are minimal or have constant mean curvature, along with some recent results. We will do this from a mathematical point of view with a general readership in mind.

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.

scholarly journals Biharmonic constant mean curvature surfaces in Killing submersions

2018 ◽  
Vol 133 ◽  
pp. 91-101
Author(s):  
Stefano Montaldo ◽  
Irene I. Onnis ◽  
Apoena Passos Passamani
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces
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