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

In this paper, we show that a noncompact gradient shrinking soliton to the List flow has at most quadratic decay for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S = R-\alpha_n| \nabla \varphi|^2}$$\end{document}. 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].