Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ANCIENT SOLUTIONS OF CODIMENSION TWO SURFACES WITH CURVATURE PINCHING IN ℝ4

  • Ji, Zhengchao (Center of Mathematical Sciences Zhejiang University)
  • Received : 2019.08.03
  • Accepted : 2020.01.03
  • Published : 2020.07.31
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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 [26] and we also remove the condition that the second fundamental form is uniformly bounded when t ∈ (-∞, -1).

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References

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