On the Complete 2-Dimensional λ-Translators with a Second Fundamental form of Constant Length

Abstract

In this article we study the two-dimensional complete λ-translators immersed in the Euclidean space ℝ3 and Minkovski space ℝ31 . We obtain two classification theorems: one for two-dimensional complete λ-translators x: M2 → ℝ3 and one for two-dimensional complete space-like λ-translators x: M2 → ℝ31 , with a second fundamental form of constant length.

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Correspondence to Xingxiao Li.

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Supported by Foundation of Natural Sciences of China (11671121, 11871197 and 11971153).

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Li, X., Qiao, R. & Liu, Y. On the Complete 2-Dimensional λ-Translators with a Second Fundamental form of Constant Length. Acta Math Sci 40, 1897–1914 (2020). https://doi.org/10.1007/s10473-020-0618-3

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Key words

  • singular solution
  • mean curvature flow
  • second fundamental form
  • λ-translator
  • classification

2010 MR Subject Classification

  • 53C44
  • 53C40