Regularity and Curvature Estimate for List’s Flow in Four Dimension

In this paper we study the List’s flow on compact manifold such that the scalar curvature is bounded. At first, we establish a time derivative bound for solution to the heat equation, based on this, we derive the existence of a cutoff function whose time derivative and Laplacian are bounded. Based on the above results, we prove the backward Pseudolocality theorem in dimension four for the List’s flow. As applications, we can obtain that the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} norm of the Riemannian curvature operator is bounded and also get the limit behavior of the List’s flow.