Communications in Analysis and Geometry

Volume 29 (2021)

Number 6

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

Pages: 1475 – 1508



Man-Chun Lee (Department of Mathematics, Chinese University of Hong Kong)

John Man Shun Ma (Department of Mathematical Sciences, University of Copenhagen, Denmark)


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