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On Bernstein–Heinz–Chern–Flanders inequalities
Published online by Cambridge University Press: 01 March 2008
Abstract
We 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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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 457 - 464
- Copyright
- Copyright © Cambridge Philosophical Society 2008
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