Properties of Warped Product Gradient Yamabe Solitons.

In this paper, we study gradient Yamabe solitons realized as warped product manifolds. We apply the maximum principle to find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product manifold. By slightly modifying Li–Yau's technique, we can handle the drifted Laplacian and thus find different gradient estimates for the warping function according to the sign of the (constant) scalar curvature of the fiber manifold. We close the article with a theorem stating the nonexistence of gradient Yamabe solitons on top of warped products with a base manifold satisfying certain analytical hypothesis. [ABSTRACT FROM AUTHOR]