  In this paper, we discuss uniqueness and backward uniqueness for mean
curvature flow of non-compact manifolds. We use an energy argument to prove two
uniqueness theorems for mean curvature flow with possibly unbounded curvatures.
These generalize the results by Chen and Yin. Using similar method, we also
obtain a uniqueness result on Ricci flows. A backward uniqueness theorem is
also proved for mean curvature flow with bounded curvatures.
