The conformal Yamabe constant of product manifolds
  Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h). 
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
math.DG math.AP