Uniqueness theorems for non-compact mean curvature flow with possibly unbounded curvatures

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 in [5]. 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.

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Received 30 September 2017

Accepted 31 January 2019

Published 11 January 2022