Abstract:
We prove that the modulus of mean curvature of the leaves of a transversely oriented
foliation of codimension one with a generalized Reeb component on an oriented smooth
closed three-dimensional Riemannian manifold cannot be everywhere smaller than a certain
positive constant depending on the volume, the maximum value of the sectional curvature,
and the injectivity radius of the manifold. This means that foliations with
small modulus of
mean curvature of the leaves are taut.
Keywords:foliations, three-dimensional manifolds, mean curvature.
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