The asymptotic behavior of symplectic mean curvature flow with pinched curvatures in CP2

摘要

It was proved by Han-Li-Yang [4] that the mean curvature flow of symplectic surfaces with suitably pinched curvatures in CP2 has a longtime solution and converges to a holomorphic curve as the time approaches infinity. In this note, we give a refinement of this theorem. We prove that the evolving surface becomes more and more umbilical and the limit surface is in fact CP1. As a consequence, the initial surface is symplectically isotopic to CP1. (C) 2015 Elsevier Inc. All rights reserved.