Best Sobolev Constants and Manifolds with Positive Scalar Curvature Metrics

We study the Yamabe invariant of manifolds which admit metrics of positive scalar curvature. Analysing 'best Sobolev constants' we give a technique to find positive lower bounds for the invariant. We apply these ideas to show that for any compact Riemannian manifold (Nn,g) of positive scalar curvature there is a positive constant K =K(N, g), which depends only on (N, g), such that for any compact manifold Mm, the Yamabe invariant of Mm x Nnis no less than K times the invariant ofSn + m. We will find some estimates for the constant K in the case N =Sn. [PUBLICATION ABSTRACT]