Bounds on volume growth of geodesic balls for Einstein warped products
  The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped product. In particular, we present an obstruction for the existence of such a class of manifolds. 
A. Barros, R. Batista and E. Ribeiro Jr
math.DG