On extremal function of a modulus of a foliation

Abstract

We investigate the properties of a modulus of a foliation on a Riemannian manifold. We give necessary and sufficient conditions for the existence of an extremal function and state some of its properties. We obtain the integral formula which, in a sense, combines the integral over the manifold with integral over the leaves. We state the relation between an extremal function and the geometry of distribution orthogonal to a foliation.