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 Ancient solutions of Codimension two surfaces with Curvature Pinching in R^4 Bull. Korean Math. Soc.Published online February 28, 2020 Zhengchao Ji Zhejiang University Abstract : We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in \cite{RS} and we also remove the condition that the second fundamental form is uniformly bounded when $t\in(-\infty, -1)$. Keywords : ancient solutions; curvature Pinching MSC numbers : 53C44, 35K55 Full-Text :