Foliations on closed three-dimensional Riemannian manifolds with small modulus of mean curvature of the leaves

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.