Classification of gradient Yamabe soliton hypersurfaces of space forms

Abstract

In this paper we investigate gradient Yamabe solitons, either steady or shrinking, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on the norm of their second fundamental form. Those solitons satisfying an additional condition, that could be constant mean curvature or the number of critical points of the potential function being at most one, are fully classified. Our argument is based on the weak Omori-Yau principle for the drifted Laplacian on Riemannian manifolds.