Lower bounds for the scalar curvature of noncompact gradient solitons of List’s flow

Abstract

In this paper, we show that a noncompact gradient shrinking soliton to the List flow has at most quadratic decay for \({S = R-\alpha_n| \nabla \varphi|^2}\). Moreover, we prove a similar result for certain noncompact gradient steady solitons to the List flow. These generalize the results of Chow et al. [4].