Foliations and Chern-Heinz inequalities

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dc.creatorBarbosa, J. L. M.
dc.creatorBessa, G. Pacelli
dc.creatorMontenegro, J Fabio
dc.date2006-01-09
dc.date2006-05-12
dc.date.accessioned2026-07-07T09:37:07Z
dc.date.available2026-07-07T09:37:07Z
dc.descriptionWe extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $Ω\subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.
dc.descriptionThis paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0601198
dc.identifierhttp://arxiv.org/abs/math/0601198
dc.identifierMath. Proc. Camb. Phil. Soc. 144, (2008), 457-464
dc.identifierdoi:10.1017/S0305004107000643
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160350
dc.subjectDifferential Geometry
dc.titleFoliations and Chern-Heinz inequalities
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