Lambda constant and Ground states of Perelman's W-functional

In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized $\lambda$ constant. The other results are about the existence of ground states of generalized $F$-functional and W-functional both on a complete non-compact Riemannian manifold $(M,g)$ with positive injectivity radius and with Ricci curvature bounded from below. Our main results are Theorems 2,3 and 7. For the existence of the ground states we use Lions' concentration-compactness method.