On codimension-one foliations of constant mean curvature (Q910019)

Let F be a codimension-one transversely oriented foliation of a compact manifold M. Denote by Mean(F) the set of all functions f: \(M\to R\) which can occur as the mean curvature of the leaves with respect to any Riemannian metric on M. Denote also by CF the union of all continuous families of compact leaves of F. Theorem 1. If \(0\in Mean(F)\), then Mean(F) contains all functions f such that \(f(x)\cdot f(y)<0\) for some x and y of M. Theorem 2. If each connected component of \(M\setminus CF\) is a Novikov component of F, then Mean(F) contains functions constant along leaves.