Foliations and Chern-Heinz inequalities
نویسندگان
چکیده
We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of C2-functions to leaves of transversally oriented codimension one C2-foliations of Riemannian manifolds. That extends partially Salavessa’s work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri [3] and Barbosa-GomesSilveira [2] 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 ⊂ R2 in terms of its inradius) for embedded tubular neighborhoods of simple curves of Rn. Mathematics Subject Classification (2000): 58C40, 53C42
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