Results related to the transverse Yamabe problem

Abstract

Let [Formula: see text] be a Riemannian minimal foliation. The transverse Yamabe problem is to find a metric [Formula: see text] in the basic conformal class of [Formula: see text] such that the transverse scalar curvature of [Formula: see text] is constant. We first study the uniqueness of the solutions of the transverse Yamabe problem. As a generalization of the transverse Yamabe problem, we study the problem of prescribing transverse scalar curvature by using geometric flow. We then prove a version of conformal Schwarz lemma on [Formula: see text]. Finally, we consider the transverse Yamabe soliton, which is the self-similar solution of the transverse Yamabe flow.